signature stringlengths 16 32 | problem_type stringclasses 12
values | optimization_type stringclasses 3
values | graph stringlengths 52 2.28k | solution stringlengths 235 4.05k | cost_hamiltonian stringlengths 11 5.66k | ansatz_id int64 1 18 | number_of_qubits int64 1 16 | number_of_layers int64 1 4 | exact_solution stringlengths 155 2.61k | circuit_with_params stringlengths 126 44.7k | circuit_with_symbols stringlengths 146 19.5k ⌀ | problem_specific_attributes stringclasses 116
values | adaptive_process stringlengths 33 186k | qiskit_pauli_strings listlengths 1 177 | qiskit_coefficients listlengths 1 177 | improvement_ratio float64 0 1 | optimized_params listlengths 2 278 | optimization_info dict | total_iterations int64 1 500 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3d627635058abf5b6bb9c53f69a1c86d | connected_components | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 3, "target": 4}, {"source": 3, "target": 7}, {"source": 3, "target":... | {"states": [63, 511], "expectation_value": -2.0702588516857356, "params": [[-0.0599], [0.062200000000000005]], "bitstrings": ["111000000", "000000000"], "total_optimization_steps": 10, "probabilities": [0.003179104768408564, 0.0033136167255936105], "optimization_time": 1.0138466358184814} | -1.5 * (Z(0) @ Z(1)) + 0.5 * (Z(2) @ Z(1)) + -1.5 * (Z(2) @ Z(0)) + -3.5 * (Z(3) @ Z(4)) + -3.5 * (Z(6) @ Z(4)) + -2.0 * (Z(6) @ Z(3)) + -3.5 * (Z(7) @ Z(4)) + -2.0 * (Z(7) @ Z(3)) + -2.0 * (Z(7) @ Z(6)) + -3.5 * (Z(5) @ Z(4)) + 0.5 * (Z(5) @ Z(3)) + 0.5 * (Z(5) @ Z(6)) + 0.5 * (Z(5) @ Z(7)) + -3.5 * (Z(8) @ Z(4)) + 0.... | 1 | 9 | 1 | {"smallest_eigenvalues": [-26.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -23.0, "smallest_bitstrings": ["000000000"], "largest_eigenvalue": 27.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(1.1398176200223498) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(0.3319500365686569) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(0.3319500365686574) q[1];
rx(1.0443828489871696) q[1];
rz(1.1398176200223498) q[2];
cx q[0], q[2];
rz(0.331950... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
bit[9] c;
qubit[9] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
h q[8];
cx q[1], q[0];
rz(x0) q[0];
cx q[1], q[0];
cx q[... | {"node": 6} | {"circuits": [], "gradients": []} | [
"IIIIIIIZZ",
"IIIIIIZZI",
"IIIIIIZIZ",
"IIIIZZIII",
"IIZIZIIII",
"IIZIIZIII",
"IZIIZIIII",
"IZIIIZIII",
"IZZIIIIII",
"IIIZZIIII",
"IIIZIZIII",
"IIZZIIIII",
"IZIZIIIII",
"ZIIIZIIII",
"ZIIIIZIII",
"ZIZIIIIII",
"ZZIIIIIII",
"ZIIZIIIII",
"IIIIIIIZI",
"IIIIIIIIZ",
"IIIIIIZII",
"... | [
-1.5,
0.5,
-1.5,
-3.5,
-3.5,
-2,
-3.5,
-2,
-2,
-3.5,
0.5,
0.5,
0.5,
-3.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-3,
1,
1,
1,
1,
1
] | 0.562351 | [
1.1398176200223498,
0.3319500365686569,
0.5835460342127498,
0.6613740611221639,
-0.15588570491585693,
-0.3429066033154878,
1.0443828489871694
] | {
"n_parameters": 7,
"n_qubits": 9,
"optimal_eigenvalue": -26,
"target_ratio": 0.97,
"target_value": -25.22
} | 185 |
ed17940d27aebadda70c31c5b11d2e16 | matching | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 0, "id": 3}, {"bipartite": 1, "id": 4}, {"bipartite": 1, "id": 5}, {"bipartite": 1, "id": 6}, {"bipartite": 1, "id": 7}], "edges": [{"weight": 9, "source": 0, "t... | {"states": [442, 218], "expectation_value": -12.430252022015267, "params": [[-0.028800000000000003, -0.0313, -0.0129], [0.038200000000000005, 0.0475, 0.035500000000000004]], "bitstrings": ["001000101", "100100101"], "total_optimization_steps": 10, "probabilities": [0.0060558589831438804, 0.007033437322857238], "optimiz... | 4.5 * (Z(0) @ Z(1)) + 4.5 * (Z(2) @ Z(0)) + 4.5 * (Z(4) @ Z(2)) + 4.5 * (Z(3) @ Z(2)) + 4.5 * (Z(3) @ Z(4)) + 4.5 * (Z(5) @ Z(0)) + 4.5 * (Z(5) @ Z(2)) + 4.5 * (Z(6) @ Z(1)) + 4.5 * (Z(6) @ Z(5)) + 4.5 * (Z(8) @ Z(4)) + 4.5 * (Z(7) @ Z(3)) + 4.5 * (Z(7) @ Z(8)) + 6.0 * Z(1) + 9.0 * Z(0) + 15.5 * Z(2) + 11.0 * Z(4) + 7.... | 1 | 9 | 3 | {"smallest_eigenvalues": [-70.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -61.5, "smallest_bitstrings": ["100100101"], "largest_eigenvalue": 128.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(-0.15866672171331941) q[0];
cx q[1], q[0];
h q[2];
cx q[0], q[2];
rz(-0.15866672171331941) q[2];
cx q[0], q[2];
h q[3];
h q[4];
cx q[2], q[4];
rz(-0.15866672171331941) q[4];
cx q[2], q[4];
cx q[2], q[3];
rz(-0.15866672171331941) q[3];
c... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "perfect_bipartite", "extra": "{\"left_nodes\": [0, 1, 2, 3], \"right_nodes\": [4, 5, 6, 7]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIZZ",
"IIIIIIZIZ",
"IIIIZIZII",
"IIIIIZZII",
"IIIIZZIII",
"IIIZIIIIZ",
"IIIZIIZII",
"IIZIIIIZI",
"IIZZIIIII",
"ZIIIZIIII",
"IZIIIZIII",
"ZZIIIIIII",
"IIIIIIIZI",
"IIIIIIIIZ",
"IIIIIIZII",
"IIIIZIIII",
"IIIIIZIII",
"IIIZIIIII",
"IIZIIIIII",
"ZIIIIIIII",
"IZIIIIIII"
] | [
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
6,
9,
15.5,
11,
7.5,
13,
2,
1.5,
9
] | 0.971003 | [
-0.15866672171331941,
-1.0809071203107758,
-0.30064965839619345,
-0.5102877140178146,
-0.8733998782451885,
1.0885724300439001,
-1.0913168284595332,
0.13810257412133115,
0.9133195435550004,
1.5142771870202085,
-0.5131275809009203,
-1.1831791592560787,
-0.05769660481193879,
-1.33952116695893... | {
"n_parameters": 30,
"n_qubits": 9,
"optimal_eigenvalue": -70.5,
"target_ratio": 0.97,
"target_value": -68.385
} | 275 |
58fa04385078dcdc0b5f9361c481400a | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 1, "target": 4}, {"source": 2, "target"... | {"states": [207, 205], "expectation_value": -0.6342479415594341, "params": [0.6247, 0.1705, 0.874, 0.3271, 0.3098, 0.3884, 0.3269, 0.4011, 0.8151, 0.4052, 0.6392, 0.12010000000000001, 0.5835, -0.30710000000000004, 0.8366, -0.2591, 0.6077, 0.1626, 0.8371000000000001, 0.35300000000000004, 0.27790000000000004, 0.390300000... | 0.25 * (Z(0) @ Z(1)) + 0.25 * (Z(0) @ Z(2)) + 0.25 * (Z(1) @ Z(2)) + -0.25 * (Z(0) @ Z(1) @ Z(2)) + 0.25 * (Z(3) @ Z(4)) + 0.25 * (Z(3) @ Z(5)) + 0.25 * (Z(4) @ Z(5)) + -0.25 * (Z(3) @ Z(4) @ Z(5)) + 0.25 * (Z(0) @ Z(3)) + 0.25 * (Z(6) @ Z(0)) + 0.25 * (Z(6) @ Z(3)) + -0.25 * (Z(6) @ Z(0) @ Z(3)) + 0.125 * (Z(1) @ Z(4)... | 18 | 8 | 3 | {"smallest_eigenvalues": [-2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125, -2.125], "number_of_smallest_eigenvalues": 16, "first_excited_energy": -1.125, "smallest_bitstrings": ["00110010", "01000110", "01010001", "01110000", "10001001", "01010100",... | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rx(0.47101618974758475) q[0];
rz(-0.16827364835461855) q[0];
rx(0.48551343822356186) q[1];
rz(0.17804732572877252) q[1];
rx(0.32539434813691376) q[2];
rz(0.5457656730524693) q[2];
rx(-0.21683998807139754) q[3];
rz(0.30031640895019224) q[3];
rx(1.2220557292476708) q[4];
... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZIZ",
"IIIIIZZI",
"IIIIIZZZ",
"IIIZZIII",
"IIZIZIII",
"IIZZIIII",
"IIZZZIII",
"IIIIZIIZ",
"IZIIIIIZ",
"IZIIZIII",
"IZIIZIIZ",
"IIIZIIZI",
"IZIIIIZI",
"ZIIIIIZI",
"IZIZIIII",
"ZIIZIIII",
"ZZIIIIII",
"IZIZIIZI",
"ZIIZIIZI",
"ZZIIIIZI",
"ZZIZIIII",
"ZZIZIIZ... | [
0.25,
0.25,
0.25,
-0.25,
0.25,
0.25,
0.25,
-0.25,
0.25,
0.25,
0.25,
-0.25,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.25,
0.25,
0.25,
-0.25,
0,
0.125,
0,
0,
0.125,
0,
0.125,
0.125
] | 0.971822 | [
0.4710161897475848,
-0.09099105680982872,
0.48551343822356186,
0.17804732572877252,
0.32539434813691376,
0.5457656730524693,
-0.21683998807139754,
0.30031640895019224,
1.2220557292476708,
0.00816620436411572,
0.6463337616946943,
0.03026562494828463,
0.5393888844458095,
-0.2593316846640103,... | {
"n_parameters": 71,
"n_qubits": 8,
"optimal_eigenvalue": -2.125,
"target_ratio": 0.97,
"target_value": -2.06125
} | 45 |
1d36f605f450bd24c53bed4c61ab6422 | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"capacity": 1, "source": 0, "target": 3}, {"capacity": 2, "source": 0, "target": 4}, {"capacity": 1, "source": 1, "target": 2}, {"capacity": 2, "source": 1, "target": 6... | {"states": [51, 35], "expectation_value": -0.6990192403016737, "params": [[0.0722, 0.061000000000000006, 0.0654], [-0.06860000000000001, -0.0511, -0.0492]], "bitstrings": ["1001100", "1011100"], "total_optimization_steps": 10, "probabilities": [0.013967852646237365, 0.014448856389640254], "optimization_time": 3.7291078... | -0.25 * (Z(0) @ Z(3)) + -0.25 * (Z(4) @ Z(3)) + -0.5 * (Z(4) @ Z(0)) + -0.5 * (Z(2) @ Z(4)) + -0.25 * (Z(1) @ Z(2)) + 1.0 * (Z(6) @ Z(0)) + -0.5 * (Z(6) @ Z(1)) + -0.5 * (Z(5) @ Z(3)) + -0.5 * (Z(5) @ Z(4)) + -0.5 * (Z(5) @ Z(1)) + -0.25 * (Z(5) @ Z(6)) + -1.0 * Z(3) + -0.25 * Z(0) + -0.75 * Z(4) + 0.25 * Z(2) + 0.25 *... | 1 | 7 | 3 | {"smallest_eigenvalues": [-6.0, -6.0], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -5.0, "smallest_bitstrings": ["1011100", "1001100"], "largest_eigenvalue": 7.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
cx q[3], q[0];
rz(-0.44173747837386507) q[0];
cx q[3], q[0];
h q[4];
cx q[3], q[4];
rz(-0.44173747837386507) q[4];
cx q[3], q[4];
cx q[0], q[4];
rz(0.005603409297500889) q[4];
cx q[0], q[4];
cx q[4], q[2];
rz(0.005603409297500889) q[2];
c... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"source": 0, "sink": 6} | {"circuits": [], "gradients": []} | [
"IIIZIIZ",
"IIZZIII",
"IIZIIIZ",
"IIZIZII",
"IIIIZZI",
"ZIIIIIZ",
"ZIIIIZI",
"IZIZIII",
"IZZIIII",
"IZIIIZI",
"ZZIIIII",
"IIIZIII",
"IIIIIIZ",
"IIZIIII",
"IIIIZII",
"IIIIIZI",
"ZIIIIII",
"IZIIIII"
] | [
-0.25,
-0.25,
-0.5,
-0.5,
-0.25,
1,
-0.5,
-0.5,
-0.5,
-0.5,
-0.25,
-1,
-0.25,
-0.75,
0.25,
0.25,
0.25,
1.25
] | 0.970536 | [
-0.44173747837386507,
0.005603409297500889,
0.05836178307980425,
-1.201402489306377,
-0.9317048549953064,
0.7320633774444789,
0.772973794919639,
-1.6652911638748984,
-0.7518283058778058,
0.06520245980832098,
0.12228192436712314,
-0.10637680738364871,
-0.2779417698846335,
1.5718265483768925... | {
"n_parameters": 24,
"n_qubits": 7,
"optimal_eigenvalue": -6,
"target_ratio": 0.97,
"target_value": -5.82
} | 91 |
44db6493095286b918fb0c5bac33de1d | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 0, "target": 5}, {"source": 1, "target": 2}, {"source": 2, "target": 3}, {"source": 2, "ta... | {"states": [12, 44], "expectation_value": -2.3315010912557774, "params": [[[0.5488000000000001, 0.12810000000000002], [0.5585, 0.1311], [0.8047000000000001, 0.0023], [0.0028, 0.5967], [0.8036000000000001, 0.0014], [0.8037000000000001, -0.0012000000000000001], [0.0023, 0.5991000000000001], [0.0029000000000000002, 0.5796... | 0.25 * (Z(0) @ Z(1)) + 0.25 * (Z(0) @ Z(2)) + 0.25 * (Z(1) @ Z(2)) + -0.25 * (Z(0) @ Z(1) @ Z(2)) + 0.125 * (Z(4) @ Z(3)) + 0.125 * (Z(5) @ Z(3)) + 0.125 * (Z(3) @ Z(6)) + 0.125 * (Z(4) @ Z(5)) + 0.125 * (Z(4) @ Z(6)) + 0.125 * (Z(5) @ Z(6)) + -0.125 * (Z(4) @ Z(5) @ Z(3)) + -0.125 * (Z(4) @ Z(3) @ Z(6)) + -0.125 * (Z(... | 1 | 8 | 2 | {"smallest_eigenvalues": [-3.875, -3.875, -3.875], "number_of_smallest_eigenvalues": 3, "first_excited_energy": -2.875, "smallest_bitstrings": ["10010111", "01011011", "11010011"], "largest_eigenvalue": 7.125} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rz(1.1114879293616777) q[0];
ry(0.15685993350026523) q[0];
rz(-1.2753559774581484) q[0];
rz(1.6455463798734922) q[1];
ry(0.12439450381357361) q[1];
rz(-2.0806830828243723) q[1];
rz(1.9810033602527488) q[2];
ry(2.948676107721393) q[2];
rz(-1.039626053423473) q[2];
rz(1.6... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZIZ",
"IIIIIZZI",
"IIIIIZZZ",
"IIIZZIII",
"IIZIZIII",
"IZIIZIII",
"IIZZIIII",
"IZIZIIII",
"IZZIIIII",
"IIZZZIII",
"IZIZZIII",
"IZZIZIII",
"IZZZIIII",
"IZZZZIII",
"IIIZIIIZ",
"IIZIIIZI",
"ZIIIIZII",
"IIIIIIIZ",
"IIIIIIZI",
"IIIIIZII",
"IIIIZIII",
"IIIZIII... | [
0.25,
0.25,
0.25,
-0.25,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.5,
0.5,
0.5,
-0.25,
-0.25,
-0.25,
-0.625,
-0.125,
-0.125,
-0.625,
-1
] | 0.972455 | [
0.40466514957797073,
0.2601706792456252,
0.0888412715111685,
0.2573921016905544,
1.8051101402836665,
0.08347576028210325,
0.030504361917943496,
0.08039412607444499,
1.381450409563023,
-0.1699186896737985,
1.1033417399647076,
0.012564086284400422,
0.18792404571706298,
0.07017314689331701,
... | {
"n_parameters": 28,
"n_qubits": 8,
"optimal_eigenvalue": -3.875,
"target_ratio": 0.97,
"target_value": -3.75875
} | 19 |
7e799239f8573f120a2c5e15cda2e88f | vertex_cover | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 1}, {"source": 1, "target": 4}]} | {"states": [14, 7], "expectation_value": -2.4964641631109394, "params": null, "bitstrings": ["10001", "11000"], "total_optimization_steps": 19, "probabilities": [0.06634837994070204, 0.9303663571679487], "optimization_time": 8.287782907485962} | 0.5 * (Z(0) @ Z(2)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(1) @ Z(0)) + 0.5 * (Z(4) @ Z(1)) + 0.0 * Z(2) + -1.0 * Z(0) + 0.0 * Z(3) + -0.5 * Z(1) + 0.0 * Z(4) | 1 | 5 | 1 | {"smallest_eigenvalues": [-2.5, -2.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -1.5, "smallest_bitstrings": ["10001", "11000"], "largest_eigenvalue": 3.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[5] q;
ry(-0.013661432647873829) q[0];
rz(-pi) q[0];
h q[1];
ry(-0.47799463725369296) q[1];
h q[2];
ry(1.609883237122917) q[2];
h q[3];
ry(1.609883237122917) q[3];
h q[4];
cx q[4], q[1];
ry(0.47799463725369296) q[1];
cx q[4], q[1];
ry(-0.6440649203767641) q[1];
ry(0.9857223264... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[5] c;\nqubit[5] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nry(-1.5681) q[0];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\n", "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[5] c;\nqubit[5]... | [
"IIZIZ",
"IZIIZ",
"IIIZZ",
"ZIIZI",
"IIZII",
"IIIIZ",
"IZIII",
"IIIZI",
"ZIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0,
-1,
0,
-0.5,
0
] | 0.994711 | [
-1.5961244559276881,
1.609883237122917,
-0.9559892745073859,
0.7778346010594781,
-0.4321667361998622,
0.4157754507244771,
-0.42379636835380385,
0.245207488748664,
-0.0379388834944252,
0.03472662903914467,
0.0730459640739915,
0.07797912356133081,
-0.0856693429277921
] | {
"n_parameters": 13,
"n_qubits": 5,
"optimal_eigenvalue": -2.5,
"target_ratio": 0.97,
"target_value": -2.425
} | 1 |
c12dc8bfc0d8e8bc2e65cda825a741ab | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}], "edges": [{"capacity": 2, "source": 0, "target": 1}, {"capacity": 1, "source": 0, "target": 2}, {"capacity": 1, "source": 1, "target": 2}]} | {"states": [3, 1], "expectation_value": -0.11018709011519463, "params": [[-0.0402, -0.028200000000000003, -0.08020000000000001], [0.055200000000000006, 0.020800000000000003, 0.0673]], "bitstrings": ["100", "110"], "total_optimization_steps": 10, "probabilities": [0.13434759204846883, 0.14508861480303417], "optimization... | -0.5 * (Z(0) @ Z(1)) + -0.25 * (Z(2) @ Z(1)) + 0.75 * (Z(2) @ Z(0)) + -0.25 * Z(1) + -0.25 * Z(0) + 0.5 * Z(2) | 1 | 3 | 3 | {"smallest_eigenvalues": [-2.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -1.0, "smallest_bitstrings": ["110"], "largest_eigenvalue": 2.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[3] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.98693634562561) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(0.5702754027205156) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(0.5702754027205152) q[1];
rx(0.1809670407241956) q[1];
rz(-0.0605909341297176) q[2];
cx q[0], q[2];
rz(0.5702754... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x... | {"source": 0, "sink": 2} | {"circuits": [], "gradients": []} | [
"IZZ",
"ZZI",
"ZIZ",
"IZI",
"IIZ",
"ZII"
] | [
-0.5,
-0.25,
0.75,
-0.25,
-0.25,
0.5
] | 0.970753 | [
0.98693634562561,
0.5702754027205156,
-0.0605909341297176,
0.01052034470793032,
0.1809670407241956,
-0.4210489548362983,
0.17941461010927579,
-0.5310091518833534,
-0.24571524346239182,
1.169259756964969,
0.8653272313101511,
0.8751350731179494,
-0.4970495411829845,
-1.6475907910109493,
1.... | {
"n_parameters": 15,
"n_qubits": 3,
"optimal_eigenvalue": -2,
"target_ratio": 0.97,
"target_value": -1.94
} | 68 |
12210bdb8f7c5877d15ce0dea7afc09c | vertex_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 1, "target": 4}, {"source": 1, "target": 6}, {"source": 2, "target":... | {"states": [797, 541], "expectation_value": -2.964683808546474, "params": [[[1.6013000000000002, 0.0021000000000000003], [1.5623, 0.0019], [0.14450000000000002, 0.0099], [0.5475, 0.0027], [0.1437, 0.009300000000000001], [1.603, 0.0035], [1.5891000000000002, 0.0007], [1.5999, 0.0019], [0.14880000000000002, 0.00520000000... | 0.5 * (Z(0) @ Z(2)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(1) @ Z(4)) + 0.5 * (Z(6) @ Z(1)) + 0.5 * (Z(8) @ Z(2)) + 0.5 * (Z(9) @ Z(2)) + 0.5 * (Z(9) @ Z(4)) + 0.5 * (Z(5) @ Z(3)) + 0.5 * (Z(5) @ Z(8)) + 0.5 * (Z(7) @ Z(4)) + 0.5 * (Z(7) @ Z(8)) + -1.0 * Z(2) + -0.5 * Z(0) + -0.5 * Z(3) + -1.0 * Z(4) + -0.5 * Z(1) + 0.0 * Z(... | 1 | 10 | 1 | {"smallest_eigenvalues": [-5.5, -5.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -4.5, "smallest_bitstrings": ["0011101010", "0111100010"], "largest_eigenvalue": 11.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
rx(3.2406260760516545) q[0];
rz(0.9483410122927294) q[0];
rx(-0.026273057328679128) q[1];
rz(-1.3303679328036595) q[1];
rx(-0.14266395752737124) q[2];
rz(1.057464151807452) q[2];
rx(0.053260050418974136) q[3];
rz(-0.18805960992949444) q[3];
rx(0.3615812544627283) q[4];... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x2;
input float[64] x3;
input float[6... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIZIZ",
"IIIIIIZIIZ",
"IIIIIZIIZI",
"IIIZIIIIZI",
"IZIIIIIZII",
"ZIIIIIIZII",
"ZIIIIZIIII",
"IIIIZIZIII",
"IZIIZIIIII",
"IIZIIZIIII",
"IZZIIIIIII",
"IIIIIIIZII",
"IIIIIIIIIZ",
"IIIIIIZIII",
"IIIIIZIIII",
"IIIIIIIIZI",
"IIIZIIIIII",
"IZIIIIIIII",
"ZIIIIIIIII",
"IIIIZIIIII"... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1,
-0.5,
-0.5,
-1,
-0.5,
0,
-1,
-0.5,
-0.5,
-0.5
] | 0.972489 | [
3.2406260760516545,
0.9483410122927294,
-0.026273057328679128,
-1.3303679328036595,
-0.14266395752737124,
1.057464151807452,
0.053260050418974136,
-0.18805960992949444,
0.3615812544627283,
1.1069936612866198,
2.953677049246105,
0.4452666946092829,
2.8862702832968403,
-1.3189156741702894,
... | {
"n_parameters": 19,
"n_qubits": 10,
"optimal_eigenvalue": -5.5,
"target_ratio": 0.97,
"target_value": -5.335
} | 27 |
a617cd4648156ddc77f993201a7a952c | kclique | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 0, "target": 7}, {"source": 1, "ta... | {"states": [70, 7], "expectation_value": -12.373769903873796, "params": [[0.0129, 0.022500000000000003, 0.0079, 0.0125], [-0.028200000000000003, -0.0519, -0.052700000000000004, -0.0439]], "bitstrings": ["10111001", "11111000"], "total_optimization_steps": 10, "probabilities": [0.008112079983223441, 0.008966988056707065... | 2.75 * (Z(0) @ Z(1)) + 2.75 * (Z(2) @ Z(1)) + 2.75 * (Z(2) @ Z(0)) + 2.75 * (Z(3) @ Z(1)) + 2.75 * (Z(3) @ Z(0)) + 2.75 * (Z(3) @ Z(2)) + 2.75 * (Z(4) @ Z(1)) + 2.75 * (Z(4) @ Z(0)) + 2.75 * (Z(4) @ Z(2)) + 2.75 * (Z(4) @ Z(3)) + 3.0 * (Z(5) @ Z(1)) + 3.0 * (Z(5) @ Z(0)) + 3.0 * (Z(5) @ Z(2)) + 3.0 * (Z(5) @ Z(3)) + 3.... | 9 | 8 | 4 | {"smallest_eigenvalues": [-24.75], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -21.75, "smallest_bitstrings": ["11111000"], "largest_eigenvalue": 135.25} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.016051595018557085) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(0.016051595018557085) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(0.016051595018557085) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(0.016051595018557085) q[3];
cx q[1], ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"k": 5} | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZZI",
"IIIIIZIZ",
"IIIIZIZI",
"IIIIZIIZ",
"IIIIZZII",
"IIIZIIZI",
"IIIZIIIZ",
"IIIZIZII",
"IIIZZIII",
"IIZIIIZI",
"IIZIIIIZ",
"IIZIIZII",
"IIZIZIII",
"IIZZIIII",
"IZIIIIZI",
"IZIIIIIZ",
"IZIIIZII",
"IZIIZIII",
"IZIZIIII",
"IZZIIIII",
"ZIIIIIZI",
"ZIIIIII... | [
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
3,
3,
3,
3,
3,
3,
3,
3,
3,
3,
3,
3,
2.75,
3,
3,
3,
2.75,
2.75,
-7,
-7.25,
-7,
-7,
-7,
-6.25,
-6.25,
-6.75
] | 0.976479 | [
0.016051595018557085,
-0.044725556110224884,
-1.5942489739862034,
-1.511915062604028,
1.942486051428569,
1.7812596979441973,
-1.4758902744393279,
0.463896267873675,
0.4666780978923133,
-1.0713581426797705,
-2.0979600597052888,
1.374106261390757,
-0.36896266833425195,
0.11673470776900458,
... | {
"n_parameters": 28,
"n_qubits": 8,
"optimal_eigenvalue": -24.75,
"target_ratio": 0.97,
"target_value": -24.0075
} | 78 |
4c5a23f8c8a34bc9c0e926b6ce68cf56 | connected_components | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 4}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 2, "ta... | {"states": [124, 127], "expectation_value": -1.9824099301492069, "params": [[-0.0785], [0.0786]], "bitstrings": ["0000011", "0000000"], "total_optimization_steps": 10, "probabilities": [0.014303046136399709, 0.014303046136399709], "optimization_time": 0.5492565631866455} | -2.5 * (Z(0) @ Z(1)) + -2.5 * (Z(2) @ Z(1)) + -2.0 * (Z(2) @ Z(0)) + 1.5 * (Z(4) @ Z(1)) + -2.5 * (Z(4) @ Z(0)) + -2.5 * (Z(4) @ Z(2)) + -2.5 * (Z(3) @ Z(1)) + 1.0 * (Z(3) @ Z(0)) + 1.0 * (Z(3) @ Z(2)) + -2.5 * (Z(3) @ Z(4)) + -1.5 * (Z(5) @ Z(6)) + 0.5 * Z(1) + 0.5 * Z(0) + 0.5 * Z(2) + 0.5 * Z(4) + 0.5 * Z(3) + 1.0 *... | 1 | 7 | 1 | {"smallest_eigenvalues": [-17.5, -17.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -16.5, "smallest_bitstrings": ["0000000", "0000011"], "largest_eigenvalue": 20.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(-0.008907998117038513) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(-0.008907998117038513) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(0.0030026574133024085) q[2];
cx q[0], q[2];
h q[3];
h q[4];
cx q[1], q[4];
rz(0.012160051034437798) q[4]... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
bit[7] c;
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[1], q[0];
rz(x0) q[0];
cx q[1], q[0];
c... | {"node": 5} | {"circuits": [], "gradients": []} | [
"IIIIIZZ",
"IIIIZZI",
"IIIIZIZ",
"IIZIIZI",
"IIZIIIZ",
"IIZIZII",
"IIIZIZI",
"IIIZIIZ",
"IIIZZII",
"IIZZIII",
"ZZIIIII",
"IIIIIZI",
"IIIIIIZ",
"IIIIZII",
"IIZIIII",
"IIIZIII",
"ZIIIIII",
"IZIIIII"
] | [
-2.5,
-2.5,
-2,
1.5,
-2.5,
-2.5,
-2.5,
1,
1,
-2.5,
-1.5,
0.5,
0.5,
0.5,
0.5,
0.5,
1,
-1
] | 0.970908 | [
-0.008907998117038513,
0.0030026574133024085,
0.012160051034437798,
0.017311852319611208,
0.10260007464896775,
-1.5737503648108313,
1.580037135188816,
1.5454240929634577
] | {
"n_parameters": 8,
"n_qubits": 7,
"optimal_eigenvalue": -17.5,
"target_ratio": 0.97,
"target_value": -16.974999999999998
} | 75 |
56bf2b9b5079d42e66a4e14293694014 | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 0, "id": 3}, {"bipartite": 0, "id": 4}, {"bipartite": 0, "id": 5}, {"bipartite": 0, "id": 6}, {"bipartite": 1, "id": 7}, {"bipartite": 1, "id": 8}, {"bipartite":... | {"states": [1745, 1681], "expectation_value": -65.23018612784095, "params": [0.6618, 0.17600000000000002, 0.9978, 0.0143, 0.9938, 0.0342, 0.7914, 0.2195, 0.9985, 0.0427, 0.7911, 0.22010000000000002, -0.0024000000000000002, 0.6598, 1.0079, 0.0115, -0.0059, 0.518, 0.005, 0.13720000000000002, 0.7903, 0.26130000000000003, ... | 8.0 * (Z(1) @ Z(3)) + 8.0 * (Z(2) @ Z(3)) + 8.0 * (Z(2) @ Z(1)) + 8.0 * (Z(0) @ Z(4)) + 8.0 * (Z(5) @ Z(4)) + 8.0 * (Z(7) @ Z(4)) + 8.0 * (Z(7) @ Z(0)) + 8.0 * (Z(6) @ Z(7)) + 8.0 * (Z(8) @ Z(1)) + 8.0 * (Z(10) @ Z(2)) + 8.0 * (Z(11) @ Z(5)) + 8.0 * (Z(11) @ Z(10)) + 3.0 * Z(3) + 17.5 * Z(1) + 17.0 * Z(2) + 15.0 * Z(4)... | 16 | 12 | 2 | {"smallest_eigenvalues": [-157.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -132.5, "smallest_bitstrings": ["100101101110"], "largest_eigenvalue": 184.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[12] q;
rx(0.38080245237496735) q[0];
rz(0.02758723353883319) q[0];
rx(1.181041379555914) q[1];
rz(0.14430224124918034) q[1];
cx q[1], q[0];
rz(0.022505404665084328) q[0];
cx q[1], q[0];
rx(-0.20472868232146732) q[0];
rz(0.24966133270202917) q[0];
rz(0.014987493321678397) q[1]... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum_bipartite", "extra": "{\"left_nodes\": [0, 1, 2, 3, 4, 5, 6], \"right_nodes\": [7, 8, 9, 10, 11, 12, 13, 14]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIIZIZI",
"IIIIIIIIZZII",
"IIIIIIIIIZZI",
"IIIIIIIZIIIZ",
"IIIIIIZZIIII",
"IIIIZIIZIIII",
"IIIIZIIIIIIZ",
"IIIIZZIIIIII",
"IIIZIIIIIIZI",
"IZIIIIIIIZII",
"ZIIIIIZIIIII",
"ZZIIIIIIIIII",
"IIIIIIIIZIII",
"IIIIIIIIIIZI",
"IIIIIIIIIZII",
"IIIIIIIZIIII",
"IIIIIIIIIIIZ",
"IIIIIIZII... | [
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
3,
17.5,
17,
15,
1,
3.5,
17.5,
-7.5,
-5.5,
3,
9.5,
-14.5
] | 0.970081 | [
0.38080245237496735,
0.05009263820391778,
1.181041379555914,
0.14430224124918034,
1.9308877648993459,
-0.11852614931728009,
-0.1920930027405437,
0.1146910644878712,
1.6362987414456447,
-0.1851733409544238,
-0.5970393911872476,
-0.061882449062761996,
0.04365754900695417,
-0.0174532568734356... | {
"n_parameters": 67,
"n_qubits": 12,
"optimal_eigenvalue": -157.5,
"target_ratio": 0.97,
"target_value": -152.775
} | 27 |
a20be77afa1a8b9b75f27972fb6e9517 | min_cut | vqe | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"capacity": 5, "source": 0, "target": 3}, {"capacity": 6, "source": 0, "target": 5}, {"capacity": 2, "source": 0, "target": 6}, {"capacity": 2, "source": 0, ... | {"states": [73, 75], "expectation_value": -16.656036797726205, "params": [-0.0088, 0.9593, 0.7847000000000001, 0.0068000000000000005, 0.0037, 0.8875000000000001, 0.0024000000000000002, 0.9078, 0.7891, 0.1826, -0.0008, 0.6888000000000001, 0.5307000000000001, 0.47140000000000004, 0.7928000000000001, 0.0074, 0.00480000000... | -1.25 * (Z(0) @ Z(3)) + -1.5 * (Z(5) @ Z(0)) + -0.25 * (Z(6) @ Z(3)) + -0.5 * (Z(6) @ Z(0)) + 3.5 * (Z(7) @ Z(0)) + -1.0 * (Z(7) @ Z(6)) + -0.5 * (Z(1) @ Z(5)) + -1.75 * (Z(1) @ Z(6)) + -1.25 * (Z(1) @ Z(7)) + -3.5 * (Z(2) @ Z(3)) + -0.25 * (Z(2) @ Z(5)) + -0.5 * (Z(2) @ Z(1)) + -0.5 * (Z(4) @ Z(1)) + -0.75 * (Z(4) @ Z... | 3 | 8 | 4 | {"smallest_eigenvalues": [-17.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -16.0, "smallest_bitstrings": ["10110100"], "largest_eigenvalue": 17.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rx(-0.05785398922763691) q[0];
rz(0.9342280145004445) q[0];
rx(0.7626187134539208) q[1];
rz(-0.24053467267746909) q[1];
rx(-0.10035809769432782) q[2];
rz(0.6211498284047625) q[2];
rx(0.04463559473375353) q[3];
rz(0.8788715835127476) q[3];
rx(0.8867672592479486) q[4];
rz... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"source": 0, "sink": 7} | {"circuits": [], "gradients": []} | [
"IIIIZIIZ",
"IIZIIIIZ",
"IZIIZIII",
"IZIIIIIZ",
"ZIIIIIIZ",
"ZZIIIIII",
"IIZIIIZI",
"IZIIIIZI",
"ZIIIIIZI",
"IIIIZZII",
"IIZIIZII",
"IIIIIZZI",
"IIIZIIZI",
"IIIZIZII",
"IIIIZIII",
"IIIIIIIZ",
"IIZIIIII",
"IZIIIIII",
"ZIIIIIII",
"IIIIIIZI",
"IIIIIZII",
"IIIZIIII"
] | [
-1.25,
-1.5,
-0.25,
-0.5,
3.5,
-1,
-0.5,
-1.75,
-1.25,
-3.5,
-0.25,
-0.5,
-0.5,
-0.75,
-1,
-0.25,
-0.75,
-1.5,
1.25,
1.5,
-0.5,
1.25
] | 0.978259 | [
-0.05785398922763691,
0.9626868323019014,
0.7626187134539207,
0.07050497449428902,
-0.10035809769432782,
1.126467781728492,
0.044635594733753524,
0.6411558748450237,
0.8867672592479487,
0.1939324997068545,
-0.10644275659624078,
0.5923681216939789,
0.8686606758937725,
0.5371592941047285,
... | {
"n_parameters": 89,
"n_qubits": 8,
"optimal_eigenvalue": -17,
"target_ratio": 0.97,
"target_value": -16.49
} | 13 |
712b030d217f3cf9b2b341027ce3b496 | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}], "edges": [{"weight": 8, "source": 0, "target": 1}, {"weight": 11, "source": 0, "target": 7}, {"weight": 14, "source": 1, "target": 6}, {"weight": 3, "source... | {"states": [219, 218], "expectation_value": -71.03949686819102, "params": [0.06380000000000001, -0.201, 0.07400000000000001, -0.2102, 0.44370000000000004, -0.0068000000000000005, 0.4751, -0.0068000000000000005, 0.4242, -0.014100000000000001, 0.4635, -0.0102, -0.0019, 0.2015, -0.0071, 0.2051, 0.45330000000000004, -0.029... | 5.0 * (Z(0) @ Z(1)) + 5.0 * (Z(2) @ Z(0)) + 5.0 * (Z(3) @ Z(4)) + 5.0 * (Z(5) @ Z(2)) + 5.0 * (Z(5) @ Z(3)) + 5.0 * (Z(6) @ Z(4)) + 5.0 * (Z(7) @ Z(1)) + 5.0 * (Z(7) @ Z(6)) + 5.0 * (Z(8) @ Z(1)) + 5.0 * (Z(8) @ Z(2)) + 5.0 * (Z(8) @ Z(5)) + 5.0 * (Z(8) @ Z(7)) + 10.5 * Z(1) + 4.0 * Z(0) + 12.0 * Z(2) + 7.0 * Z(4) + 1.... | 5 | 9 | 4 | {"smallest_eigenvalues": [-72.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -65.0, "smallest_bitstrings": ["100100101"], "largest_eigenvalue": 134.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(-0.11626367191495617) q[0];
rz(-0.2106040854003126) q[0];
rx(0.9478855789126086) q[1];
rz(-0.06828684283665343) q[1];
rx(-0.20148789490429764) q[2];
rz(0.24190586838730788) q[2];
rx(-0.10600745945522326) q[3];
rz(0.24682421348931705) q[3];
rx(0.7705790951013602) q[4]... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x100;
input float[64] x101;
input float[64] x102;
input float[64] x103;
input float[64] x104;
input float[64] x105;
input float[64] x106;
input float[64] x107;
input float[64] x108;
input float[64] x109;
i... | {"matching": "maximum", "extra": "{\"n\": 9}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIZZ",
"IIIIIIZIZ",
"IIIIZZIII",
"IIIZIIZII",
"IIIZIZIII",
"IIZIZIIII",
"IZIIIIIZI",
"IZZIIIIII",
"ZIIIIIIZI",
"ZIIIIIZII",
"ZIIZIIIII",
"ZZIIIIIII",
"IIIIIIIZI",
"IIIIIIIIZ",
"IIIIIIZII",
"IIIIZIIII",
"IIIIIZIII",
"IIIZIIIII",
"IIZIIIIII",
"IZIIIIIII",
"ZIIIIIIII"
] | [
5,
5,
5,
5,
5,
5,
5,
5,
5,
5,
5,
5,
10.5,
4,
12,
7,
1.5,
13,
0.5,
10.5,
15
] | 0.971796 | [
-0.11626367191495618,
-0.03173752259946515,
0.9478855789126086,
-0.10405674410918156,
-0.20148789490429764,
0.16198685409452146,
-0.10600745945522325,
0.24035094405800145,
0.7705790951013602,
-0.3696644980084714,
0.5459902919862265,
-0.19463096022212167,
-0.27051526918250374,
-0.2029262882... | {
"n_parameters": 174,
"n_qubits": 9,
"optimal_eigenvalue": -72,
"target_ratio": 0.97,
"target_value": -69.84
} | 83 |
-3157302381660211115 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8], "hyperedges": [[1, 5], [3, 6], [0, 5], [8, 5], [1, 3], [1, 6], [0, 7], [8, 7], [1, 2], [3, 4], [5, 7], [2, 6], [1, 4], [0, 8], [2, 5]]} | {"states": [481, 482], "expectation_value": -0.0243691610085646, "params": [[0.0267], [-0.030600000000000002]], "bitstrings": ["000011110", "000011101"], "total_optimization_steps": 10, "probabilities": [0.0019979953159408185, 0.0019979953159408185], "optimization_time": 0.698986291885376} | 0.5 * (Z(1) @ Z(5)) + 0.5 * (Z(3) @ Z(1)) + 0.5 * (Z(6) @ Z(1)) + 0.5 * (Z(6) @ Z(3)) + 0.5 * (Z(0) @ Z(5)) + 0.5 * (Z(8) @ Z(5)) + 0.5 * (Z(8) @ Z(0)) + 0.5 * (Z(7) @ Z(5)) + 0.5 * (Z(7) @ Z(0)) + 0.5 * (Z(7) @ Z(8)) + 0.5 * (Z(2) @ Z(5)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(2) @ Z(6)) + 0.5 * (Z(4) @ Z(1)) + 0.5 * (Z(4) ... | 1 | 9 | 1 | {"smallest_eigenvalues": [-3.5, -3.5, -3.5, -3.5, -3.5, -3.5], "number_of_smallest_eigenvalues": 6, "first_excited_energy": -2.5, "smallest_bitstrings": ["000011101", "000011110", "111100010", "111100001", "011100011", "100011100"], "largest_eigenvalue": 7.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
cx q[5], q[1];
rz(0.49710203531280295) q[1];
cx q[5], q[1];
cx q[1], q[3];
rz(0.49710203531280295) q[3];
cx q[1], q[3];
cx q[5], q[0];
rz(0.49710203531280295) q[0];
cx q[5], q[0];
h q[6];
cx q[1], q[6];
rz(0.49710203531280... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
bit[9] c;
qubit[9] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
h q[8];
cx q[5], q[1];
rz(x0) q[1];
cx q[5], q[1];
cx q[1], q[3];
rz(x0) q[3];
cx q[1], q[3];
cx q[1], q[6];
rz(x0) q[6];
cx q[1], q[6];... | null | {"circuits": [], "gradients": []} | [
"IIIZIIIZI",
"IIIIIZIZI",
"IIZIIIIZI",
"IIZIIZIII",
"IIIZIIIIZ",
"ZIIZIIIII",
"ZIIIIIIIZ",
"IZIZIIIII",
"IZIIIIIIZ",
"ZZIIIIIII",
"IIIZIIZII",
"IIIIIIZZI",
"IIZIIIZII",
"IIIIZIIZI",
"IIIIZZIII",
"IIIZIIIII",
"IIIIIIIZI",
"IIIIIZIII",
"IIZIIIIII",
"IIIIIIIIZ",
"ZIIIIIIII",
"... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0.521922 | [
0.49710203531280295,
-1.7510023132553513e-8,
-0.6162569686825089
] | {
"n_parameters": 3,
"n_qubits": 9,
"optimal_eigenvalue": -3.5,
"target_ratio": 0.97,
"target_value": -3.395
} | 96 |
-6170143923129228437 | hypermaxcut | adaptive_vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7], "hyperedges": [[0, 2, 4], [1, 5], [3, 5, 6], [0, 3], [1, 2, 3], [0, 5], [4, 7], [2, 3, 5]]} | {"states": [53, 60], "expectation_value": -2.749487076024844, "params": null, "bitstrings": ["11001010", "11000011"], "total_optimization_steps": 53, "probabilities": [0.05608097171249614, 0.8054378771726384], "optimization_time": 79.60331678390503} | 0.16666666666666666 * (Z(0) @ Z(2)) + 0.16666666666666666 * (Z(4) @ Z(2)) + 0.16666666666666666 * (Z(4) @ Z(0)) + 0.16666666666666666 * (Z(1) @ Z(2)) + 0.16666666666666666 * (Z(5) @ Z(2)) + 0.5 * (Z(5) @ Z(0)) + 0.5 * (Z(5) @ Z(1)) + 0.3333333333333333 * (Z(3) @ Z(2)) + 0.5 * (Z(3) @ Z(0)) + 0.16666666666666666 * (Z(3)... | 1 | 8 | 1 | {"smallest_eigenvalues": [-2.9999999999999996], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.6666666666666665, "smallest_bitstrings": ["11000011"], "largest_eigenvalue": 6.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
ry(-0.12003282375748284) q[0];
h q[1];
ry(-0.7036416366232529) q[1];
h q[2];
ry(1.689937242978624) q[2];
h q[3];
h q[4];
h q[5];
cx q[5], q[0];
ry(0.12003282375748284) q[0];
cx q[5], q[0];
ry(-0.21536199390707664) q[0];
cx q[3], q[0];
ry(0.21536199390707664) q[0... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[8] c;\nqubit[8] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\nry(1.4449) q[2];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = measure q[... | [
"IIIIIZIZ",
"IIIZIZII",
"IIIZIIIZ",
"IIIIIZZI",
"IIZIIZII",
"IIZIIIIZ",
"IIZIIIZI",
"IIIIZZII",
"IIIIZIIZ",
"IIIIZIZI",
"IIZIZIII",
"IZZIIIII",
"IZIIZIII",
"ZIIZIIII",
"IIIIIZII",
"IIIIIIIZ",
"IIIZIIII",
"IIIIIIZI",
"IIZIIIII",
"IIIIZIII",
"IZIIIIII",
"ZIIIIIII"
] | [
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.5,
0.3333333333333333,
0.5,
0.16666666666666666,
0.3333333333333333,
0.16666666666666666,
0.16666666666666666,
0.5,
0.5,
0.16666666666666674,
0.16666666666666663,
0.16666... | 0.97751 | [
1.689937242978624,
-0.24006564751496567,
1.2908432739075522,
-1.4072832732465057,
-0.4307239878141533,
1.1241849211424557,
-0.7285963603189985,
0.08813997978865121,
-0.8027900727794686,
1.0636410974108739,
-0.71361962222048,
0.468879011091531,
-0.5487983758686867,
0.41154812646595734,
-0... | {
"n_parameters": 43,
"n_qubits": 8,
"optimal_eigenvalue": -2.9999999999999996,
"target_ratio": 0.97,
"target_value": -2.9099999999999997
} | 20 |
2783967b1611213b3e7795654a08824b | vertex_cover | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 3}, {"source": 0, "target": 5}, {"source": 1, "target": 3}, {"source": 1, "target": 4}, {"source": 1, "target": 5}, {"source": 2, "target": 4}, ... | {"states": [97, 112], "expectation_value": -3.9963269419040746, "params": null, "bitstrings": ["0011110", "0001111"], "total_optimization_steps": 29, "probabilities": [0.06635596786049659, 0.9302847332721631], "optimization_time": 31.777088165283203} | 0.5 * (Z(0) @ Z(3)) + 0.5 * (Z(5) @ Z(0)) + 0.5 * (Z(1) @ Z(3)) + 0.5 * (Z(1) @ Z(5)) + 0.5 * (Z(4) @ Z(3)) + 0.5 * (Z(4) @ Z(5)) + 0.5 * (Z(4) @ Z(1)) + 0.5 * (Z(2) @ Z(4)) + 0.5 * (Z(6) @ Z(2)) + -1.0 * Z(3) + -0.5 * Z(0) + -1.0 * Z(5) + -1.0 * Z(1) + -1.5 * Z(4) + -0.5 * Z(2) + 0.0 * Z(6) | 1 | 7 | 4 | {"smallest_eigenvalues": [-4.0, -4.0, -4.0, -4.0, -4.0], "number_of_smallest_eigenvalues": 5, "first_excited_energy": -3.0, "smallest_bitstrings": ["0011110", "0111010", "0001111", "1110100", "1100101"], "largest_eigenvalue": 10.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
ry(1.4476455626952967) q[0];
h q[1];
ry(1.4476455626952967) q[1];
h q[2];
ry(-0.059126059586819345) q[3];
rz(-pi) q[3];
cx q[1], q[3];
ry(0.09486143994178287) q[3];
cx q[1], q[3];
ry(0.008187482699304706) q[3];
h q[4];
ry(-1.6038831393838435) q[4];
ry(-0.0591260... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[7] c;\nqubit[7] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nry(-1.5708) q[4];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = measure q[6];\n", ... | [
"IIIZIIZ",
"IZIIIIZ",
"IIIZIZI",
"IZIIIZI",
"IIZZIII",
"IZZIIII",
"IIZIIZI",
"IIZIZII",
"ZIIIZII",
"IIIZIII",
"IIIIIIZ",
"IZIIIII",
"IIIIIZI",
"IIZIIII",
"IIIIZII",
"ZIIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1,
-0.5,
-1,
-1,
-1.5,
-0.5,
0
] | 0.996122 | [
-1.6038831393838435,
-1.4168088272662944,
1.4476455626952967,
-1.1273306452707597,
0.7286646700863632,
-0.18972287988356573,
-0.36076103541921345,
0.3420029579089602,
-0.42645300423253624,
0.2659988647826904,
-0.04303709360162987,
0.09904893961194784,
0.1611605001101052,
0.1474386520393811... | {
"n_parameters": 15,
"n_qubits": 7,
"optimal_eigenvalue": -4,
"target_ratio": 0.97,
"target_value": -3.88
} | 1 |
24ec85ceb3f94374e977a871ddcf35bc | edge_cover | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"source": 0, "target": 1}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 1, "target": 5}, {"source": 2, "target": 4}, {"source": 2, "target": 5}, {"source": ... | {"states": [50, 60], "expectation_value": -3.1321770286570354, "params": null, "bitstrings": ["1001101", "1000011"], "total_optimization_steps": 36, "probabilities": [0.06225990274216573, 0.8457025003025933], "optimization_time": 43.28484129905701} | 0.125 * (Z(0) @ Z(1)) + 0.125 * (Z(0) @ Z(2)) + 0.125 * (Z(0) @ Z(3)) + 0.125 * (Z(1) @ Z(2)) + 0.125 * (Z(1) @ Z(3)) + 0.125 * (Z(2) @ Z(3)) + -0.125 * (Z(0) @ Z(1) @ Z(2)) + -0.125 * (Z(0) @ Z(1) @ Z(3)) + -0.125 * (Z(0) @ Z(2) @ Z(3)) + -0.125 * (Z(1) @ Z(2) @ Z(3)) + 0.125 * (Z(0) @ Z(1) @ Z(2) @ Z(3)) + 0.25 * (Z(... | 1 | 7 | 2 | {"smallest_eigenvalues": [-3.375], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.375, "smallest_bitstrings": ["1000011"], "largest_eigenvalue": 5.625} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
ry(-0.04176737542190623) q[0];
rz(-pi) q[0];
ry(-2.945037601850049) q[1];
rz(-pi) q[1];
h q[2];
ry(1.4906421176738867) q[2];
h q[3];
h q[4];
ry(0.6746829349540775) q[4];
h q[5];
ry(-0.2974549213254869) q[5];
cx q[3], q[5];
ry(0.2974549213254869) q[5];
cx q[3], q[5];
ry(... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[7] c;\nqubit[7] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nry(-1.5158) q[0];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = measure q[6];\n", ... | [
"IIIIIZZ",
"IIIIZIZ",
"IIIZIIZ",
"IIIIZZI",
"IIIZIZI",
"IIIZZII",
"IIIIZZZ",
"IIIZIZZ",
"IIIZZIZ",
"IIIZZZI",
"IIIZZZZ",
"IIZIIZI",
"IZIIIZI",
"IZZIIII",
"IZZIIZI",
"ZIIIZII",
"ZIZIIII",
"IZIZIII",
"IIIIIIZ",
"IIIIIZI",
"IIIIZII",
"IIIZIII",
"IIZIIII",
"IZIIIII",
"ZII... | [
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.25,
0.25,
0.25,
-0.25,
0.5,
0.5,
0.5,
-0.625,
0.125,
-0.125,
-0.125,
-0.25,
-0.25,
-0.5
] | 0.971567 | [
-1.5669187022824613,
-1.5230986125139825,
1.4906421176738867,
-0.5949098426509738,
1.0949934439908702,
1.1307724253187426,
-0.9752655168159003,
1.349365869908155,
0.5257905149682746,
0.08690217507268594,
-0.18517364442419398,
0.5584956621285644,
0.3260867579106622,
0.07577950181894219,
0... | {
"n_parameters": 24,
"n_qubits": 7,
"optimal_eigenvalue": -3.375,
"target_ratio": 0.97,
"target_value": -3.2737499999999997
} | 12 |
ced6c703f6fc42ad993c62457521a8a6 | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"capacity": 2, "source": 0, "target": 1}, {"capacity": 2, "source": 0, "target": 2}, {"capacity": 2, "source": 0, "target": 5}, {"capacity": 1, "source": 0, ... | {"states": [3, 1], "expectation_value": -0.9943841305168674, "params": [[-0.0716, -0.0852], [0.0711, 0.0781]], "bitstrings": ["11111100", "11111110"], "total_optimization_steps": 10, "probabilities": [0.00807690791938644, 0.008983622340901491], "optimization_time": 3.047116279602051} | -0.5 * (Z(0) @ Z(1)) + -0.75 * (Z(2) @ Z(1)) + -0.5 * (Z(2) @ Z(0)) + -0.5 * (Z(5) @ Z(1)) + -0.5 * (Z(5) @ Z(0)) + -0.25 * (Z(6) @ Z(0)) + -0.5 * (Z(3) @ Z(1)) + -0.25 * (Z(3) @ Z(5)) + -0.25 * (Z(3) @ Z(6)) + -0.5 * (Z(4) @ Z(5)) + 2.0 * (Z(7) @ Z(0)) + -0.25 * (Z(7) @ Z(4)) + -0.75 * Z(1) + -0.25 * Z(0) + -0.25 * Z(... | 1 | 8 | 2 | {"smallest_eigenvalues": [-9.75], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -8.75, "smallest_bitstrings": ["11111110"], "largest_eigenvalue": 6.25} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.019257244790662688) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(0.7877168041877103) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(0.019257244790662688) q[2];
cx q[0], q[2];
rz(0.4711390611845201) q[2];
rx(1.6286054759878306) q[2];
h q[3];... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
input float[64] x9;
bit[8] c;
qubit[8] ... | {"source": 0, "sink": 7} | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZZI",
"IIIIIZIZ",
"IIZIIIZI",
"IIZIIIIZ",
"IZIIIIIZ",
"IIIIZIZI",
"IIZIZIII",
"IZIIZIII",
"IIZZIIII",
"ZIIIIIIZ",
"ZIIZIIII",
"IIIIIIZI",
"IIIIIIIZ",
"IIIIIZII",
"IIZIIIII",
"IZIIIIII",
"IIIIZIII",
"IIIZIIII",
"ZIIIIIII"
] | [
-0.5,
-0.75,
-0.5,
-0.5,
-0.5,
-0.25,
-0.5,
-0.25,
-0.25,
-0.5,
2,
-0.25,
-0.75,
-0.25,
-0.25,
-0.25,
0,
0,
-0.25,
1.75
] | 0.915875 | [
0.019257244790662688,
0.7877168041877103,
0.4711390611845201,
-0.07346987499868925,
0.8629803409167578,
-0.5184398952558648,
1.6286054759878306,
0.06686996022923065,
1.0861776397855343,
0.7850543096022358,
-0.14646282643499497,
-1.831074504387705,
1.075806303014285
] | {
"n_parameters": 13,
"n_qubits": 8,
"optimal_eigenvalue": -9.75,
"target_ratio": 0.97,
"target_value": -9.4575
} | 298 |
1009275363050825591 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], "hyperedges": [[1, 2, 4, 5, 6, 8, 9, 10, 11], [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11], [2, 4, 7, 8, 9, 10], [0, 1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 7, 8, 10, 11], [1, 2, 5, 6, 7, 8, 9], [2, 3, 8, 9, 10], [2, 4, 5, 7, 8, 10, 11], [1, 2, 3, 8, 9, 11], [0, 2, 3, 6, 11], [0, 1, 2,... | {"states": [925, 989], "expectation_value": -2.3426889827424873, "params": [0.2549, 0.0044, 1.5027000000000001, 0.008400000000000001, 3.1389, 0.0016, 3.1445000000000003, 0.0024000000000000002, 3.1439000000000004, 0.004, 1.5915000000000001, 0.001, 0.529, 0.0095, 2.2841, 0.0074, 3.1444, 0.004200000000000001, 3.1441000000... | 0.16825396825396827 * (Z(1) @ Z(4)) + 0.08492063492063492 * (Z(6) @ Z(4)) + 0.03686868686868687 * (Z(6) @ Z(1)) + 0.15873015873015872 * (Z(7) @ Z(4)) + 0.06067821067821068 * (Z(7) @ Z(1)) + 0.06067821067821068 * (Z(7) @ Z(6)) + 0.10158730158730159 * (Z(8) @ Z(4)) + 0.06067821067821068 * (Z(8) @ Z(1)) + 0.03686868686868... | 3 | 12 | 1 | {"smallest_eigenvalues": [-2.5097402597402603, -2.5097402597402603], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -2.476406926406926, "smallest_bitstrings": ["010010100000", "110000100010"], "largest_eigenvalue": 12.999999999999995} | OPENQASM 3.0;
include "stdgates.inc";
qubit[12] q;
rx(-0.14696868876468855) q[0];
rz(-0.3171563528381647) q[0];
rx(1.3727780868243882) q[1];
rz(0.21358523923569184) q[1];
rx(-3.1377124870751323) q[2];
rz(0.18900101667389624) q[2];
rx(3.1093539282627365) q[3];
rz(0.13612442878867226) q[3];
rx(3.0403290944196906) q[4];
r... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIZIIZI",
"IIIIIZIZIIII",
"IIIIIZIIIIZI",
"IIIIZIIZIIII",
"IIIIZIIIIIZI",
"IIIIZZIIIIII",
"IIIZIIIZIIII",
"IIIZIIIIIIZI",
"IIIZIZIIIIII",
"IIIZZIIIIIII",
"IZIIIIIZIIII",
"IZIIIIIIIIZI",
"IZIIIZIIIIII",
"IZIIZIIIIIII",
"IZIZIIIIIIII",
"ZIIIIIIZIIII",
"ZIIIIIIIIIZI",
"ZIIIIZIII... | [
0.16825396825396827,
0.08492063492063492,
0.03686868686868687,
0.15873015873015872,
0.06067821067821068,
0.06067821067821068,
0.10158730158730159,
0.06067821067821068,
0.03686868686868687,
0.06067821067821068,
0.2115079365079365,
0.11345598845598845,
0.08012265512265512,
0.0705988455988455... | 0.970138 | [
-0.14696868876468855,
-0.26477415602898235,
1.3727780868243882,
0.14239015949046124,
3.1454728201044544,
-0.01645340205245987,
3.1093539282627365,
0.13481450887624508,
3.0403290944196906,
-0.08420535209357025,
2.1481555759990516,
0.5809009317107608,
0.04960759734958278,
0.08401287405705918... | {
"n_parameters": 33,
"n_qubits": 12,
"optimal_eigenvalue": -2.5097402597402603,
"target_ratio": 0.97,
"target_value": -2.4344480519480522
} | 14 |
e69550c833474bf45ede93c29793364e | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 3}, {"source": 1, "target": 3}, {"source": 1, "target": 5}, {"source": 2, "target": 3}, {"source": 2, "target": 5}, {"source": 2, "target": 6}, ... | {"states": [187, 179], "expectation_value": -1.8545002982275105, "params": [-0.0001, 0.3165, 0.5056, 0.0045000000000000005, 0.2228, 0.29610000000000003, 0.49770000000000003, 0.045200000000000004, 0.5037, 0.10690000000000001, 0.29700000000000004, 0.1091, -0.0051, 0.34940000000000004, 0.498, 0.0051, 0.4988, 0.0256, -0.00... | 0.5 * (Z(1) @ Z(2)) + 0.25 * (Z(3) @ Z(4)) + 0.25 * (Z(3) @ Z(5)) + 0.25 * (Z(4) @ Z(5)) + -0.25 * (Z(3) @ Z(4) @ Z(5)) + 0.0625 * (Z(0) @ Z(1)) + 0.0625 * (Z(3) @ Z(0)) + 0.0625 * (Z(0) @ Z(6)) + 0.0625 * (Z(0) @ Z(7)) + 0.0625 * (Z(3) @ Z(1)) + 0.0625 * (Z(1) @ Z(6)) + 0.0625 * (Z(1) @ Z(7)) + 0.0625 * (Z(3) @ Z(6)) ... | 16 | 9 | 4 | {"smallest_eigenvalues": [-3.8125], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.8125, "smallest_bitstrings": ["101001100"], "largest_eigenvalue": 6.1875} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(-0.12756266301791686) q[0];
rz(0.4735655294126939) q[0];
rx(0.7057245043454681) q[1];
rz(0.01739646315227371) q[1];
cx q[1], q[0];
rz(-0.17079390449201795) q[0];
cx q[1], q[0];
rx(-0.09359776567047304) q[0];
rz(0.3946108485469644) q[0];
rz(0.16138507446855765) q[1];
... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZZI",
"IIIIZZIII",
"IIIZIZIII",
"IIIZZIIII",
"IIIZZZIII",
"IIIIIIIZZ",
"IIIIIZIIZ",
"IIZIIIIIZ",
"IZIIIIIIZ",
"IIIIIZIZI",
"IIZIIIIZI",
"IZIIIIIZI",
"IIZIIZIII",
"IZIIIZIII",
"IZZIIIIII",
"IIIIIZIZZ",
"IIZIIIIZZ",
"IZIIIIIZZ",
"IIZIIZIIZ",
"IZIIIZIIZ",
"IZZIIIIIZ",
"... | [
0.5,
0.25,
0.25,
0.25,
-0.25,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
0.25,... | 0.977207 | [
-0.12756266301791686,
0.3027716249206759,
0.7057245043454681,
0.01739646315227371,
-0.02127030246383349,
0.4485978116077558,
0.7355465327503719,
0.1720628108444342,
0.5553067573265572,
0.11298983305762661,
0.04772227440995786,
-0.13462033402531828,
-0.05790695997609201,
0.37542508224080573... | {
"n_parameters": 98,
"n_qubits": 9,
"optimal_eigenvalue": -3.8125,
"target_ratio": 0.97,
"target_value": -3.698125
} | 14 |
690ab9a303c84e82b8d6c798626278a5 | connected_components | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}, {"id": 10}], "edges": [{"source": 0, "target": 2}, {"source": 1, "target": 2}, {"source": 3, "target": 4}, {"source": 3, "target": 5}, {"source": ... | {"states": [0, 832], "expectation_value": -41.41569264949275, "params": [0.7536, 0.0975, -0.0414, 0.12990000000000002, 0.7651, -0.060000000000000005, 0.4813, -0.0286, -0.003, 0.8566, 0.001, 1.1193, 0.7005, 1.022, 0.5232, 1.6599000000000002, 0.006200000000000001, 1.8054000000000001, -0.0027, 0.7349, -0.00310000000000000... | -1.5 * (Z(0) @ Z(3)) + -1.5 * (Z(1) @ Z(3)) + 0.5 * (Z(1) @ Z(0)) + -3.5 * (Z(4) @ Z(5)) + -4.0 * (Z(6) @ Z(5)) + -3.5 * (Z(6) @ Z(4)) + 1.0 * (Z(9) @ Z(5)) + -3.5 * (Z(9) @ Z(4)) + -3.5 * (Z(9) @ Z(6)) + 1.5 * (Z(2) @ Z(5)) + -3.5 * (Z(2) @ Z(4)) + -4.0 * (Z(2) @ Z(6)) + -3.5 * (Z(2) @ Z(9)) + -3.0 * (Z(8) @ Z(5)) + 1... | 6 | 10 | 2 | {"smallest_eigenvalues": [-43.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -40.0, "smallest_bitstrings": ["0010111111"], "largest_eigenvalue": 42.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
rx(1.0713131931509305) q[0];
rz(1.7862098367790207) q[0];
rx(1.0594819371364768) q[1];
rz(1.5589265290462944) q[1];
rx(0.01573601181023064) q[2];
rz(2.2817926178052783) q[2];
rx(0.6615662260196581) q[3];
rz(2.620309016787145) q[3];
rx(0.03153201728100909) q[4];
rz(-3.0... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"node": 4} | {"circuits": [], "gradients": []} | [
"IIIIIIZIIZ",
"IIIIIIZIZI",
"IIIIIIIIZZ",
"IIIIZZIIII",
"IIIZZIIIII",
"IIIZIZIIII",
"ZIIIZIIIII",
"ZIIIIZIIII",
"ZIIZIIIIII",
"IIIIZIIZII",
"IIIIIZIZII",
"IIIZIIIZII",
"ZIIIIIIZII",
"IZIIZIIIII",
"IZIIIZIIII",
"IZIZIIIIII",
"ZZIIIIIIII",
"IZIIIIIZII",
"IIZIZIIIII",
"IIZIIZIIII"... | [
-1.5,
-1.5,
0.5,
-3.5,
-4,
-3.5,
1,
-3.5,
-3.5,
1.5,
-3.5,
-4,
-3.5,
-3,
1,
1.5,
1,
-4,
1,
1,
-4,
-3,
1.5,
-3,
0.5,
0.5,
0.5,
1.5,
-2.5,
-3,
2,
-2.5,
1,
1
] | 0.970425 | [
1.0713131931509308,
0.2154135099841242,
1.0594819371364768,
-0.011869797748602046,
0.01573601181023064,
0.7109962910103812,
0.6615662260196581,
1.049512689992248,
0.031532017281009087,
1.6276333307871536,
0.011405340564087828,
1.8244243881924735,
0.033834528725764666,
0.81374651859747,
0... | {
"n_parameters": 94,
"n_qubits": 10,
"optimal_eigenvalue": -43,
"target_ratio": 0.97,
"target_value": -41.71
} | 72 |
723b73fdc30b23dba77c4958fef78f24 | vertex_cover | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 4}, {"source": 0, "target": 5}, {"source": 1, "target": 5}, {"source": 2, "target": 5}, {"source": 2, "target": 3}, ... | {"states": [113, 53], "expectation_value": -3.79062548108071, "params": null, "bitstrings": ["0001110", "1001010"], "total_optimization_steps": 46, "probabilities": [0.04769126139284315, 0.8614509210248673], "optimization_time": 35.353190660476685} | 0.5 * (Z(0) @ Z(2)) + 0.5 * (Z(4) @ Z(0)) + 0.5 * (Z(5) @ Z(2)) + 0.5 * (Z(5) @ Z(0)) + 0.5 * (Z(1) @ Z(5)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(6) @ Z(3)) + -1.0 * Z(2) + -1.0 * Z(0) + 0.0 * Z(4) + -1.0 * Z(5) + 0.0 * Z(1) + -0.5 * Z(3) + 0.0 * Z(6) | 1 | 7 | 1 | {"smallest_eigenvalues": [-4.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -3.0, "smallest_bitstrings": ["1001010"], "largest_eigenvalue": 7.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
ry(-0.3213284069120986) q[0];
h q[1];
ry(1.561227557979563) q[1];
ry(-0.5996924930716909) q[2];
rz(-pi) q[2];
h q[3];
ry(-0.3213284069120986) q[3];
h q[4];
cx q[4], q[0];
ry(0.3213284069120986) q[0];
cx q[4], q[0];
ry(-0.6920859783029909) q[0];
ry(0.858866298320... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[7] c;\nqubit[7] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nry(-1.5681) q[5];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = measure q[6];\n", ... | [
"IIIIZIZ",
"IIZIIIZ",
"IZIIZII",
"IZIIIIZ",
"IZIIIZI",
"IIIZZII",
"ZIIZIII",
"IIIIZII",
"IIIIIIZ",
"IIZIIII",
"IZIIIII",
"IIIIIZI",
"IIIZIII",
"ZIIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1,
-1,
0,
-1,
0,
-0.5,
0
] | 0.976117 | [
-1.5228681084041154,
-1.391331881335179,
1.561227557979563,
-0.6426568138241971,
0.4893931357312403,
-0.39231862825062086,
0.7389463251778208,
-0.5995347001047401,
0.3967606414427418,
0.38756318595233574,
-0.14652558977380725,
-0.24590209038459773,
0.14523805156870565,
0.8404560952239467,
... | {
"n_parameters": 29,
"n_qubits": 7,
"optimal_eigenvalue": -4,
"target_ratio": 0.97,
"target_value": -3.88
} | 10 |
-2692663721775254224 | hypermaxcut | adaptive_vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8], "hyperedges": [[8, 1], [0, 8, 2], [2, 3, 4, 7], [8, 4], [8, 5], [3, 6]]} | {"states": [97, 99], "expectation_value": -2.3005466726825876, "params": null, "bitstrings": ["110011110", "110011100"], "total_optimization_steps": 76, "probabilities": [0.14512773478928898, 0.6158416290090808], "optimization_time": 145.47570705413818} | 0.5 * (Z(8) @ Z(1)) + 0.16666666666666666 * (Z(0) @ Z(8)) + 0.16666666666666666 * (Z(2) @ Z(8)) + 0.16666666666666666 * (Z(2) @ Z(0)) + 0.08333333333333333 * (Z(3) @ Z(2)) + 0.5 * (Z(4) @ Z(8)) + 0.08333333333333333 * (Z(4) @ Z(2)) + 0.08333333333333333 * (Z(4) @ Z(3)) + 0.08333333333333333 * (Z(7) @ Z(2)) + 0.08333333... | 1 | 9 | 1 | {"smallest_eigenvalues": [-2.583333333333333, -2.583333333333333, -2.583333333333333], "number_of_smallest_eigenvalues": 3, "first_excited_energy": -2.5, "smallest_bitstrings": ["000100001", "000000111", "110011100"], "largest_eigenvalue": 3.9999999999999996} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
ry(-0.21368102071230427) q[0];
h q[1];
ry(-0.8365433786104083) q[1];
h q[2];
ry(1.1724415387981126) q[2];
h q[3];
h q[4];
ry(-0.7346865163986053) q[4];
h q[5];
ry(-0.18783218235630042) q[5];
h q[6];
ry(-0.18783218235630042) q[6];
cx q[3], q[6];
ry(0.187832182356... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[9] c;\nqubit[9] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\nh q[8];\nry(1.1408) q[2];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = m... | [
"ZIIIIIIZI",
"ZIIIIIIIZ",
"ZIIIIIZII",
"IIIIIIZIZ",
"IIIIIZZII",
"ZIIIZIIII",
"IIIIZIZII",
"IIIIZZIII",
"IZIIIIZII",
"IZIIIZIII",
"IZIIZIIII",
"ZIIZIIIII",
"IIZIIZIII",
"IIIIIIIZI",
"ZIIIIIIII",
"IIIIIIIIZ",
"IIIIIIZII",
"IIIIIZIII",
"IIIIZIIII",
"IZIIIIIII",
"IIIZIIIII",
"... | [
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.08333333333333333,
0.5,
0.08333333333333333,
0.08333333333333333,
0.08333333333333333,
0.08333333333333333,
0.08333333333333333,
0.5,
0.5,
0,
0.16666666666666674,
0.16666666666666666,
0.29166666666666663,
0.125,
... | 0.975348 | [
1.1724415387981126,
-0.37566436471260084,
1.4831057580330378,
-1.6730867572208166,
-1.4693730327972105,
0.1019589705756815,
-0.7790459870784905,
0.8164304677546135,
-0.8483455077280122,
0.5773000671263295,
-0.2102889164254818,
-0.42736204142460854,
0.013368210730224275,
0.00246486571189877... | {
"n_parameters": 69,
"n_qubits": 9,
"optimal_eigenvalue": -2.583333333333333,
"target_ratio": 0.97,
"target_value": -2.505833333333333
} | 18 |
e9af1a9f112f5a53fb57fbd0d9beb1bf | connected_components | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 1, "target": 2}, {"source": 3, "target": 4}, {"source": 5, "target": 6}]} | {"states": [63, 62], "expectation_value": -8.023090846737073, "params": [[[-0.0025, 3.1588000000000003], [0.0028, -0.0026000000000000003], [0.0026000000000000003, 0.0027], [0.0024000000000000002, -0.0149], [-1.6182, 0.0026000000000000003], [-0.0027, 0.0022]]], "bitstrings": ["000000", "000001"], "total_optimization_ste... | -1.5 * (Z(0) @ Z(1)) + -1.5 * (Z(2) @ Z(1)) + -1.5 * (Z(2) @ Z(0)) + -1.0 * (Z(3) @ Z(4)) + 0.5 * Z(1) + 0.5 * Z(0) + 0.5 * Z(2) + 0.5 * Z(4) + 0.5 * Z(3) + -0.5 * Z(5) | 15 | 6 | 1 | {"smallest_eigenvalues": [-8.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -7.5, "smallest_bitstrings": ["000001"], "largest_eigenvalue": 3.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
ry(0.05694439345088629) q[0];
ry(0.07964889352568336) q[1];
ry(-0.011315584505599684) q[2];
ry(0.12547947242218094) q[3];
ry(-2.261873266415947) q[4];
ry(-0.05231947757244105) q[5];
cx q[5], q[0];
cx q[4], q[5];
cx q[3], q[4];
cx q[2], q[3];
cx q[1], q[2];
cx q[0], q[1]... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
input float[64] x9;
bit[6] c;
qubit[6] q;
ry(x0) q[0];
ry(x1) q[1];
ry(x2) q[2];
... | {"node": 6} | {"circuits": [], "gradients": []} | [
"IIIIZZ",
"IIIZZI",
"IIIZIZ",
"IZZIII",
"IIIIZI",
"IIIIIZ",
"IIIZII",
"IZIIII",
"IIZIII",
"ZIIIII"
] | [
-1.5,
-1.5,
-1.5,
-1,
0.5,
0.5,
0.5,
0.5,
0.5,
-0.5
] | 0.970689 | [
0.05694439345088629,
0.07964889352568336,
-0.011315584505599684,
0.12547947242218094,
-2.261873266415947,
-0.05231947757244105,
3.0493721289513904,
0.019216606340822288,
-0.08003579411712652,
0.02644848824165674,
0.06864849289218175
] | {
"n_parameters": 11,
"n_qubits": 6,
"optimal_eigenvalue": -8.5,
"target_ratio": 0.97,
"target_value": -8.245
} | 13 |
563fe0ee35342a7adbb26905c51bef72 | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 0, "id": 3}, {"bipartite": 0, "id": 4}, {"bipartite": 1, "id": 5}, {"bipartite": 1, "id": 6}, {"bipartite": 1, "id": 7}, {"bipartite": 1, "id": 8}, {"bipartite":... | {"states": [430, 426], "expectation_value": -92.89957127026618, "params": [0.45380000000000004, 0.0037, 2.9015, 0.007500000000000001, 2.8954, 0.0092, 0.46280000000000004, 0.0005, 2.8953, 0.0045000000000000005, 1.0493000000000001, 0.0035, 2.9018, 0.0068000000000000005, 1.4863000000000002, 0.0071, 2.8973, 0.0034000000000... | 6.0 * (Z(2) @ Z(0)) + 6.0 * (Z(1) @ Z(0)) + 6.0 * (Z(1) @ Z(2)) + 6.0 * (Z(3) @ Z(1)) + 6.0 * (Z(4) @ Z(2)) + 6.0 * (Z(4) @ Z(3)) + 6.0 * (Z(6) @ Z(2)) + 6.0 * (Z(6) @ Z(4)) + 6.0 * (Z(5) @ Z(6)) + 6.0 * (Z(7) @ Z(2)) + 6.0 * (Z(7) @ Z(4)) + 6.0 * (Z(7) @ Z(6)) + 6.0 * (Z(8) @ Z(5)) + 6.0 * (Z(9) @ Z(8)) + 1.0 * Z(0) +... | 18 | 10 | 1 | {"smallest_eigenvalues": [-108.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -93.0, "smallest_bitstrings": ["1001010101"], "largest_eigenvalue": 186.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
rx(-0.29562429764535286) q[0];
rz(-0.2706473678377215) q[0];
rx(3.224449011006635) q[1];
rz(0.07787340345987548) q[1];
rx(3.126778875855139) q[2];
rz(-0.23573288747189666) q[2];
rx(0.18824576661061992) q[3];
rz(-0.5215299419485757) q[3];
rx(3.0790256971910437) q[4];
rz... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum_bipartite", "extra": "{\"left_nodes\": [0, 1, 2, 3, 4], \"right_nodes\": [5, 6, 7, 8, 9, 10]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIZIZ",
"IIIIIIIIZZ",
"IIIIIIIZZI",
"IIIIIIZIZI",
"IIIIIZIZII",
"IIIIIZZIII",
"IIIZIIIZII",
"IIIZIZIIII",
"IIIZZIIIII",
"IIZIIIIZII",
"IIZIIZIIII",
"IIZZIIIIII",
"IZIIZIIIII",
"ZZIIIIIIII",
"IIIIIIIIIZ",
"IIIIIIIZII",
"IIIIIIIIZI",
"IIIIIIZIII",
"IIIIIZIIII",
"IIIZIIIIII"... | [
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
6,
1,
25,
15,
1,
21.5,
20,
4.5,
10.5,
5.5,
-2
] | 0.978313 | [
-0.29562429764535275,
-0.30324560552753943,
3.224449011006635,
0.07787340345987548,
3.126778875855139,
-0.23573288747189666,
0.18824576661061992,
-0.5215299419485757,
3.0790256971910437,
0.06561753560651426,
0.4220028652374331,
-0.21606965211973272,
3.0595213656032363,
0.34440346489308127,... | {
"n_parameters": 27,
"n_qubits": 10,
"optimal_eigenvalue": -108,
"target_ratio": 0.97,
"target_value": -104.75999999999999
} | 13 |
8477355649959193433 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], "hyperedges": [[9, 4, 5, 1], [0, 5], [0, 1, 6, 9], [8, 4, 5], [3, 5, 7], [0, 1, 2, 3, 4, 9], [8, 9, 4, 1], [0, 6, 7], [8, 9, 2, 4], [0, 9, 4, 8], [9, 2, 5], [3, 6], [1, 3, 7], [8, 9, 2, 3], [9, 5, 6, 7], [8, 2, 5, 6]]} | {"states": [415, 287], "expectation_value": -3.860356265920327, "params": [0.2717, 0.7421, 0.2733, 0.0033, 1.6796, 0.4005, 1.4679, 0.002, 1.2674, -0.3398, 0.7832, 0.0078000000000000005, 0.2985, 0.7515000000000001, 0.2884, 0.009300000000000001, 0.6744, -0.6482, 0.6668000000000001, 0.0011, 1.6686, 0.3534, 1.4556, 0.0076,... | 0.36666666666666664 * (Z(9) @ Z(4)) + 0.25 * (Z(5) @ Z(4)) + 0.3333333333333333 * (Z(5) @ Z(9)) + 0.2 * (Z(1) @ Z(4)) + 0.2833333333333333 * (Z(1) @ Z(9)) + 0.08333333333333333 * (Z(1) @ Z(5)) + 0.11666666666666667 * (Z(0) @ Z(4)) + 0.2 * (Z(0) @ Z(9)) + 0.5 * (Z(0) @ Z(5)) + 0.11666666666666667 * (Z(0) @ Z(1)) + 0.166... | 5 | 10 | 1 | {"smallest_eigenvalues": [-4.033333333333333], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -3.933333333333333, "smallest_bitstrings": ["1011100000"], "largest_eigenvalue": 14.999999999999995} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
rx(0.05456441168667227) q[0];
rz(0.9144438765638458) q[0];
rx(1.858282193693357) q[1];
rz(0.5435387512412739) q[1];
rx(1.0537848418887872) q[2];
rz(-0.6153172120422163) q[2];
rx(0.010766291818456853) q[3];
rz(0.9638413998069586) q[3];
rx(0.5812319867593729) q[4];
rz(-1... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"ZIIIIZIIII",
"IIIIZZIIII",
"ZIIIZIIIII",
"IIIIIZIIZI",
"ZIIIIIIIZI",
"IIIIZIIIZI",
"IIIIIZIIIZ",
"ZIIIIIIIIZ",
"IIIIZIIIIZ",
"IIIIIIIIZZ",
"ZIIZIIIIII",
"IIIZZIIIII",
"IIIZIIIIZI",
"IIIZIIIIIZ",
"IZIIIZIIII",
"ZZIIIIIIII",
"IZIIZIIIII",
"IZIIIIIIZI",
"IZIIIIIIIZ",
"IZIZIIIIII"... | [
0.36666666666666664,
0.25,
0.3333333333333333,
0.2,
0.2833333333333333,
0.08333333333333333,
0.11666666666666667,
0.2,
0.5,
0.11666666666666667,
0.16666666666666666,
0.16666666666666666,
0.08333333333333333,
0.25,
0.41666666666666663,
0.3333333333333333,
0.25,
0.08333333333333333,
... | 0.970405 | [
0.05456441168667227,
0.6280732278538748,
1.858282193693357,
0.5343265203964427,
1.0537848418887872,
-0.5021922288713905,
0.010766291818456852,
0.6279715628259458,
0.5812319867593729,
-1.1095594265705864,
1.9113190031120815,
0.14346378693177,
1.5425896253773541,
0.3317197176593015,
1.8125... | {
"n_parameters": 50,
"n_qubits": 10,
"optimal_eigenvalue": -4.033333333333333,
"target_ratio": 0.97,
"target_value": -3.912333333333333
} | 52 |
a5c40d068011c4e4e7f2c8be1bf9e74e | min_cut | adaptive_vqe | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}], "edges": [{"capacity": 6, "source": 0, "target": 1}, {"capacity": 4, "source": 0, "target": 4}, {"capacity": 3, "source": 1, "target": 2}, {"capacity": 5, "source": 1, "target": 3}, {"capacity": 4, "so... | {"states": [16, 1], "expectation_value": -6.193832856874677, "params": null, "bitstrings": ["01111", "11110"], "total_optimization_steps": 16, "probabilities": [0.16217477587726464, 0.8147160154427896], "optimization_time": 8.827763080596924} | -1.5 * (Z(0) @ Z(1)) + -1.0 * (Z(4) @ Z(1)) + 1.75 * (Z(4) @ Z(0)) + -0.75 * (Z(2) @ Z(1)) + -1.25 * (Z(3) @ Z(1)) + -1.0 * (Z(3) @ Z(2)) + 1.5 * Z(1) + -0.25 * Z(0) + 0.75 * Z(4) + 0.25 * Z(2) + -2.25 * Z(3) | 1 | 5 | 2 | {"smallest_eigenvalues": [-6.75], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -4.75, "smallest_bitstrings": ["11110"], "largest_eigenvalue": 9.25} | OPENQASM 3.0;
include "stdgates.inc";
qubit[5] q;
h q[0];
ry(-0.403513744402808) q[0];
rz(-pi) q[1];
ry(-0.26244175595439895) q[1];
rz(-pi) q[2];
ry(-0.029488094427819626) q[2];
h q[3];
ry(-1.4713482188317892) q[3];
h q[4];
cx q[4], q[0];
ry(0.403513744402808) q[0];
cx q[4], q[0];
ry(-1.102703959745292) q[0];
ry(1.6020... | null | {"source": 0, "sink": 4} | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[5] c;\nqubit[5] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nry(-1.5708) q[3];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\n", "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[5] c;\nqubit[5]... | [
"IIIZZ",
"ZIIZI",
"ZIIIZ",
"IIZZI",
"IZIZI",
"IZZII",
"IIIZI",
"IIIIZ",
"ZIIII",
"IIZII",
"IZIII"
] | [
-1.5,
-1,
1.75,
-0.75,
-1.25,
-1,
1.5,
-0.25,
0.75,
0.25,
-2.25
] | 0.971362 | [
-1.4713482188317892,
-0.807027488805616,
1.4911052735712893,
-1.102703959745292,
-1.7020375436318982,
-1.833778612837321,
0.221883680341239,
0.20350624481836382,
0.0010810601760510158,
0.1165906038876539
] | {
"n_parameters": 10,
"n_qubits": 5,
"optimal_eigenvalue": -6.75,
"target_ratio": 0.97,
"target_value": -6.547499999999999
} | 14 |
aaa0b19e64bf3c35281517d1fd2e9593 | vertex_cover | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"source": 0, "target": 1}, {"source": 1, "target": 2}, {"source": 2, "target": 3}, {"source": 2, "target": 5}, {"source": 2, "target": 4}]} | {"states": [39, 23], "expectation_value": -0.3603378603142312, "params": [[-0.0626, -0.046700000000000005, -0.026500000000000003], [0.0757, 0.0697, 0.0548]], "bitstrings": ["011000", "101000"], "total_optimization_steps": 10, "probabilities": [0.021879456620974364, 0.022552922979383064], "optimization_time": 2.77986717... | 0.5 * (Z(0) @ Z(1)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(5) @ Z(2)) + 0.5 * (Z(4) @ Z(2)) + -0.5 * Z(1) + 0.0 * Z(0) + -1.5 * Z(2) + 0.0 * Z(3) + 0.0 * Z(5) + 0.0 * Z(4) | 1 | 6 | 3 | {"smallest_eigenvalues": [-3.5, -3.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -2.5, "smallest_bitstrings": ["011000", "101000"], "largest_eigenvalue": 4.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.3082490255491387) q[0];
cx q[1], q[0];
rz(-0.4813792428916286) q[0];
rx(-0.0708269652138156) q[0];
h q[2];
cx q[1], q[2];
rz(0.3082490255491387) q[2];
cx q[1], q[2];
rz(0.38370389231516544) q[1];
rx(-0.07082696521381568) q[1];
cx q[1]... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
input float[64] x9;
bit[6] c;
qubit[6] ... | null | {"circuits": [], "gradients": []} | [
"IIIIZZ",
"IIIZZI",
"IIZZII",
"ZIIZII",
"IZIZII",
"IIIIZI",
"IIIIIZ",
"IIIZII",
"IIZIII",
"ZIIIII",
"IZIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
-0.5,
0,
-1.5,
0,
0,
0
] | 0.977854 | [
0.3082490255491387,
0.3837038923151648,
-0.48137924289163025,
0.26332802912302594,
-0.07082696521381564,
-0.3050505286502088,
0.5806483285648956,
0.6562418208675107,
0.7543675324261974,
-0.03625229813212085,
0.44867521434950836,
0.9051415988683418,
0.9758359490263386
] | {
"n_parameters": 13,
"n_qubits": 6,
"optimal_eigenvalue": -3.5,
"target_ratio": 0.97,
"target_value": -3.395
} | 18 |
8ca1cc128f26bbc587d2dbeb0c149cd8 | vertex_cover | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 4}, {"source": 0, "target": 6}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, ... | {"states": [7, 22], "expectation_value": -4.496397975823587, "params": null, "bitstrings": ["1111000", "1101001"], "total_optimization_steps": 27, "probabilities": [0.06635229672491205, 0.9303266266439268], "optimization_time": 22.416858911514282} | 0.5 * (Z(0) @ Z(1)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(2) @ Z(0)) + 0.5 * (Z(4) @ Z(1)) + 0.5 * (Z(4) @ Z(0)) + 0.5 * (Z(6) @ Z(0)) + 0.5 * (Z(6) @ Z(2)) + 0.5 * (Z(3) @ Z(1)) + 0.5 * (Z(3) @ Z(4)) + 0.5 * (Z(5) @ Z(3)) + -1.5 * Z(1) + -1.5 * Z(0) + -1.0 * Z(2) + -1.0 * Z(4) + -0.5 * Z(6) + -1.0 * Z(3) + 0.0 * Z(5) | 1 | 7 | 3 | {"smallest_eigenvalues": [-4.5, -4.5, -4.5], "number_of_smallest_eigenvalues": 3, "first_excited_energy": -3.5, "smallest_bitstrings": ["1011100", "1101001", "1111000"], "largest_eigenvalue": 11.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
ry(-0.1044186887575012) q[0];
rz(-pi) q[0];
h q[1];
ry(-1.62086699164525) q[1];
h q[2];
ry(-0.04832317967740758) q[3];
rz(-pi) q[3];
h q[4];
ry(1.5043802004688414) q[4];
h q[5];
ry(1.5043802004688414) q[5];
cx q[5], q[3];
ry(0.08766964893760334) q[3];
cx q[5], q[3];
ry(... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[7] c;\nqubit[7] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nry(-1.5708) q[1];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = measure q[6];\n", ... | [
"IIIIIZZ",
"IIIIZZI",
"IIIIZIZ",
"IIZIIZI",
"IIZIIIZ",
"ZIIIIIZ",
"ZIIIZII",
"IIIZIZI",
"IIZZIII",
"IZIZIII",
"IIIIIZI",
"IIIIIIZ",
"IIIIZII",
"IIZIIII",
"ZIIIIII",
"IIIZIII",
"IZIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1.5,
-1.5,
-1,
-1,
-0.5,
-1,
0
] | 0.993724 | [
-1.62086699164525,
-1.3938278090987974,
-1.4348034981798856,
1.5043802004688414,
-1.0020042667393492,
0.7466029713197173,
-0.1753392978752067,
-0.3045979748548337,
0.4578212070017425,
-0.5218060619904213,
0.24997306403953848,
0.09313877057308015,
0.08178973406295656,
0.07313792589671532,
... | {
"n_parameters": 17,
"n_qubits": 7,
"optimal_eigenvalue": -4.5,
"target_ratio": 0.97,
"target_value": -4.365
} | 1 |
a4b3b2771ff4e4ca105df7c0df433cd0 | vertex_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 0, "target": 7}, {"source": 1, "ta... | {"states": [64, 90], "expectation_value": -6.132306295163199, "params": [[[-0.0751, -0.28500000000000003, 0.0004, 0.0067], [-0.6867000000000001, 0.1041, 0.7001000000000001, 0.007200000000000001], [0.0, 0.030100000000000002, 0.0009000000000000001, -0.2731], [0.0035, 0.0867, -0.013300000000000001, 0.0639], [-0.0036000000... | 0.5 * (Z(0) @ Z(1)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(2) @ Z(0)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(4) @ Z(0)) + 0.5 * (Z(4) @ Z(2)) + 0.5 * (Z(7) @ Z(1)) + 0.5 * (Z(7) @ Z(0)) + 0.5 * (Z(7) @ Z(4)) + 0.5 * (Z(5) @ Z(1)) + 0.5 * (Z(5) @ Z(3)) + 0.5 * (Z(5) @ Z(4)) + 0.5 * (Z(6) @ Z(2)) + 0.5 * (Z(6) ... | 11 | 8 | 3 | {"smallest_eigenvalues": [-7.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -6.5, "smallest_bitstrings": ["10100101"], "largest_eigenvalue": 18.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
ry(-0.08628121508740876) q[0];
rz(-0.3360049035343489) q[0];
ry(-0.6957165805429221) q[1];
rz(0.18520395874586093) q[1];
cx q[1], q[0];
ry(0.7002692797292411) q[0];
rz(-0.388906925232151) q[0];
ry(0.8843233849051527) q[1];
rz(0.13682047486148696) q[1];
ry(-0.07644267254... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZZI",
"IIIIIZIZ",
"IIIIZIIZ",
"IIIIZZII",
"IIIZIIIZ",
"IIIZIZII",
"ZIIIIIZI",
"ZIIIIIIZ",
"ZIIZIIII",
"IIZIIIZI",
"IIZIZIII",
"IIZZIIII",
"IZIIIZII",
"IZZIIIII",
"IIIIIIZI",
"IIIIIIIZ",
"IIIIIZII",
"IIIIZIII",
"IIIZIIII",
"ZIIIIIII",
"IIZIIIII",
"IZIIIII... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1.5,
-2,
-2,
-1,
-1.5,
-1,
-1.5,
-0.5
] | 0.974968 | [
-0.08628121508740876,
-0.3360049035343489,
-0.6957165805429221,
0.18520395874586093,
-0.07644267254826459,
0.07058671917977896,
-0.02010867207353012,
-0.0821123878056284,
-0.035252244253960584,
0.440027603088897,
0.023516846752002482,
0.13252242502529457,
-0.08174748086251984,
0.1652447542... | {
"n_parameters": 81,
"n_qubits": 8,
"optimal_eigenvalue": -7.5,
"target_ratio": 0.97,
"target_value": -7.2749999999999995
} | 37 |
90cd45aecbe758daa031a854118281c7 | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 4}, {"source": 1, "target": 2}, {"source": 1, "target": 4}, {"source": 2, "target": 3}, {"source": 2, "target": 4}, {"source": 3, "target": 4}, ... | {"states": [58, 122], "expectation_value": -1.3928239964208848, "params": [0.0007, 0.315, 0.313, 0.166, 0.4046, 0.11080000000000001, 0.40390000000000004, 0.0077, 0.4087, -0.003, 0.4077, 0.0081, 0.0009000000000000001, 0.2852, 0.3932, 0.1812, 0.3952, 0.1198, 0.0036000000000000003, 0.29910000000000003, 0.31070000000000003... | 0.5 * (Z(1) @ Z(2)) + 0.25 * (Z(3) @ Z(1)) + 0.25 * (Z(4) @ Z(1)) + 0.25 * (Z(3) @ Z(4)) + -0.25 * (Z(3) @ Z(4) @ Z(1)) + 0.125 * (Z(3) @ Z(5)) + 0.125 * (Z(3) @ Z(6)) + 0.125 * (Z(3) @ Z(7)) + 0.125 * (Z(5) @ Z(6)) + 0.125 * (Z(5) @ Z(7)) + 0.125 * (Z(6) @ Z(7)) + -0.125 * (Z(3) @ Z(5) @ Z(6)) + -0.125 * (Z(3) @ Z(5) ... | 18 | 9 | 4 | {"smallest_eigenvalues": [-3.9375, -3.9375], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -2.9375, "smallest_bitstrings": ["110000110", "110000101"], "largest_eigenvalue": 6.0625} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(0.056912986577473866) q[0];
rz(0.3094642138848882) q[0];
rx(-0.155076333841582) q[1];
rz(0.3052202151005613) q[1];
rx(0.8584301783604933) q[2];
rz(0.08129913585944087) q[2];
rx(1.1489608051634745) q[3];
rz(-0.23794780314121378) q[3];
rx(0.6604106178284125) q[4];
rz(-... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZZI",
"IIIIIZIZI",
"IIIIZIIZI",
"IIIIZZIII",
"IIIIZZIZI",
"IIIZIZIII",
"IIZIIZIII",
"IZIIIZIII",
"IIZZIIIII",
"IZIZIIIII",
"IZZIIIIII",
"IIZZIZIII",
"IZIZIZIII",
"IZZIIZIII",
"IZZZIIIII",
"IZZZIZIII",
"IIIIIIZIZ",
"IIIIZIIIZ",
"IIIZIIIIZ",
"ZIIIIIIIZ",
"IIIIZIZII",
"... | [
0.5,
0.25,
0.25,
0.25,
-0.25,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625... | 0.975467 | [
0.05691298657747386,
0.5132692831194525,
-0.155076333841582,
0.3052202151005613,
0.8584301783604933,
0.08129913585944087,
1.1489608051634745,
-0.23794780314121378,
0.6604106178284125,
-0.031076673860656233,
0.9177511790288277,
0.32405280952797977,
0.22133575689637358,
0.16741808596700913,
... | {
"n_parameters": 99,
"n_qubits": 9,
"optimal_eigenvalue": -3.9375,
"target_ratio": 0.97,
"target_value": -3.819375
} | 36 |
1a8155b224db54664a68f055f033253f | graph_isomorphism | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}], "edges": [{"source": 1, "target": 3}]} | {"states": [55230, 47070], "expectation_value": -8.607065046012032, "params": [[-0.17880000000000001], [0.1715]], "bitstrings": ["0010100001000001", "0100100000100001"], "total_optimization_steps": 20, "probabilities": [0.0001368416516879302, 0.00013684165753380978], "optimization_time": 16.067975282669067} | 0.5 * (Z(2) @ Z(0)) + 0.5 * (Z(1) @ Z(0)) + 0.5 * (Z(1) @ Z(2)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(3) @ Z(1)) + 0.5 * (Z(6) @ Z(2)) + 0.5 * (Z(4) @ Z(0)) + 0.5 * (Z(4) @ Z(6)) + 0.5 * (Z(5) @ Z(1)) + 0.5 * (Z(5) @ Z(6)) + 0.5 * (Z(5) @ Z(4)) + 0.25 * (Z(7) @ Z(0)) + 0.5 * (Z(7) @ Z(3)) + 0.5 * (Z(7)... | 1 | 16 | 1 | {"smallest_eigenvalues": [-18.49999999999997], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -18.49999999999981, "smallest_bitstrings": ["0100100000100001"], "largest_eigenvalue": NaN} | OPENQASM 3.0;
include "stdgates.inc";
qubit[16] q;
h q[0];
h q[1];
h q[2];
cx q[0], q[2];
rz(-1.7976347027261054e-08) q[2];
cx q[0], q[2];
cx q[0], q[1];
rz(-1.7976347027261054e-08) q[1];
cx q[0], q[1];
cx q[2], q[1];
rz(-1.7976347027261054e-08) q[1];
cx q[2], q[1];
h q[3];
cx q[0], q[3];
rz(-1.7976347027261054e-08) q[... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
bit[16] c;
qubit[16] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
h q[8];
h q[9];
h q[10];
h q[11];
... | {"autoisomorphic_graph": {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 2}, {"id": 0}, {"id": 1}, {"id": 3}], "edges": [{"source": 0, "target": 3}]}} | {"circuits": [], "gradients": []} | [
"IIIIIIIIIIIIIZIZ",
"IIIIIIIIIIIIIIZZ",
"IIIIIIIIIIIIIZZI",
"IIIIIIIIIIIIZIIZ",
"IIIIIIIIIIIIZZII",
"IIIIIIIIIIIIZIZI",
"IIIIIIIIIZIIIZII",
"IIIIIIIIIIIZIIIZ",
"IIIIIIIIIZIZIIII",
"IIIIIIIIIIZIIIZI",
"IIIIIIIIIZZIIIII",
"IIIIIIIIIIZZIIII",
"IIIIIIIIZIIIIIIZ",
"IIIIIIIIZIIIZIII",
"IIIIIII... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.25,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.25,
0.5,
0.25,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.25,
0.25,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.25,
0.... | 0.891892 | [
-1.7976347027261054e-8,
-1.2399449651503569e-8,
-1.5707962915080487,
-1.5707964004599495,
1.5707963785331627,
-1.5707963408864278,
-1.5707964034514517,
1.5707963010445554
] | {
"n_parameters": 8,
"n_qubits": 16,
"optimal_eigenvalue": -18.49999999999997,
"target_ratio": 0.97,
"target_value": -17.944999999999972
} | 280 |
-308162691934680590 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7], "hyperedges": [[4, 6], [3, 6, 7], [3, 4, 7], [0, 3, 5], [0, 2], [0, 4, 5], [1, 2]]} | {"states": [199, 61], "expectation_value": -1.217077423423206, "params": [[-0.46730000000000005], [0.4187]], "bitstrings": ["00111000", "11000010"], "total_optimization_steps": 50, "probabilities": [0.019940923786775804, 0.020213442125386585], "optimization_time": 1.6853220462799072} | 0.5 * (Z(4) @ Z(6)) + 0.16666666666666666 * (Z(3) @ Z(6)) + 0.16666666666666666 * (Z(3) @ Z(4)) + 0.16666666666666666 * (Z(7) @ Z(6)) + 0.16666666666666666 * (Z(7) @ Z(4)) + 0.3333333333333333 * (Z(7) @ Z(3)) + 0.16666666666666666 * (Z(0) @ Z(4)) + 0.16666666666666666 * (Z(0) @ Z(3)) + 0.16666666666666666 * (Z(5) @ Z(4... | 1 | 8 | 1 | {"smallest_eigenvalues": [-2.5000000000000004], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.5, "smallest_bitstrings": ["11000010"], "largest_eigenvalue": 5.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[6], q[4];
rz(-1.095790797731945) q[4];
cx q[6], q[4];
cx q[6], q[3];
rz(-0.05723998934420572) q[3];
cx q[6], q[3];
cx q[4], q[3];
rz(-0.05723998934420572) q[3];
cx q[4], q[3];
h q[7];
cx q[6], q[7];
rz(-0.0572... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
bit[8] c;
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
cx q[6], q[4];
rz(x0) q[4];
cx q[6], q[4];
cx q[6], q[3];
rz(x1) q[3];
cx q[6], q[3];
cx q[4], q... | null | {"circuits": [], "gradients": []} | [
"IZIZIIII",
"IZIIZIII",
"IIIZZIII",
"ZZIIIIII",
"ZIIZIIII",
"ZIIIZIII",
"IIIZIIIZ",
"IIIIZIIZ",
"IIZZIIII",
"IIZIZIII",
"IIZIIIIZ",
"IIIIIZIZ",
"IIIIIZZI",
"IZIIIIII",
"IIIZIIII",
"IIIIZIII",
"ZIIIIIII",
"IIIIIIIZ",
"IIZIIIII",
"IIIIIZII",
"IIIIIIZI"
] | [
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.3333333333333333,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.3333333333333333,
0.5,
0.5,
0.16666666666666663,
0.33333333333333326,
0.4999999999999999,
... | 0.659697 | [
-1.095790797731945,
-0.05723998934420572,
-0.45858900921317475,
0.0726373231155015,
0.8245231131354819
] | {
"n_parameters": 5,
"n_qubits": 8,
"optimal_eigenvalue": -2.5000000000000004,
"target_ratio": 0.97,
"target_value": -2.4250000000000003
} | 126 |
0effcbb2abad3a5cea04794e851efa69 | vertex_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 0, "target": 6}, {"source": 1, "target":... | {"states": [146, 154], "expectation_value": -6.643229909348072, "params": [[[1.4877, 0.0077], [0.0018000000000000002, 0.0011], [1.7080000000000002, 0.002], [0.0025, 0.0074], [0.0034000000000000002, 0.0025], [1.6999000000000002, 0.0037], [1.6355000000000002, 0.0007], [-0.003, 0.0027], [1.7096, 0.0097], [0.44420000000000... | 0.5 * (Z(0) @ Z(1)) + 0.5 * (Z(3) @ Z(1)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(4) @ Z(0)) + 0.5 * (Z(6) @ Z(0)) + 0.5 * (Z(6) @ Z(3)) + 0.5 * (Z(6) @ Z(4)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(2) @ Z(4)) + 0.5 * (Z(7) @ Z(1)) + 0.5 * (Z(7) @ Z(4)) + 0.5 * (Z(7) @ Z(6)) + 0.5 * (Z(9) @ Z(4)) + 0.5 * (Z(9) @ Z(2)) + 0.5 * (Z(8) ... | 1 | 10 | 1 | {"smallest_eigenvalues": [-8.5, -8.5, -8.5, -8.5], "number_of_smallest_eigenvalues": 4, "first_excited_energy": -7.5, "smallest_bitstrings": ["1011110100", "1011100101", "0101101101", "1101100101"], "largest_eigenvalue": 23.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
rx(3.020882782460678) q[0];
rz(0.5848460207774312) q[0];
rx(0.08800709579939482) q[1];
rz(-0.37063314114788165) q[1];
rx(2.893362231525249) q[2];
rz(-0.27215624297009444) q[2];
rx(0.1283370680121939) q[3];
rz(0.45650174157219847) q[3];
rx(0.2105493280898556) q[4];
rz(0... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIIZZ",
"IIIIIIZIZI",
"IIIIIIZIIZ",
"IIIIIZIIIZ",
"IIIZIIIIIZ",
"IIIZIIZIII",
"IIIZIZIIII",
"IIIIIIIZZI",
"IIIIIZIZII",
"IIZIIIIIZI",
"IIZIIZIIII",
"IIZZIIIIII",
"ZIIIIZIIII",
"ZIIIIIIZII",
"IZIIIIZIII",
"IZIIIZIIII",
"IZZIIIIIII",
"IIZIZIIIII",
"ZIIIZIIIII",
"IIIIIIIIZI"... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1.5,
-1.5,
-1.5,
-2.5,
-1.5,
-1,
-2,
-1,
-1,
-0.5
] | 0.979688 | [
3.020882782460678,
0.5848460207774312,
0.08800709579939482,
-0.37063314114788165,
2.893362231525249,
-0.27215624297009444,
0.1283370680121939,
0.45650174157219847,
0.2105493280898556,
2.9851106710567255,
0.6746022931072954,
-0.05146585903613771,
0.13865628038107675,
0.16522318734965957,
... | {
"n_parameters": 18,
"n_qubits": 10,
"optimal_eigenvalue": -8.5,
"target_ratio": 0.97,
"target_value": -8.245
} | 23 |
ab957251534d09507f870c3a6ef42154 | community_detection | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"weight": 1, "source": 0, "target": 2}, {"weight": 1, "source": 0, "target": 5}, {"weight": 1, "source": 1, "target": 2}, {"weight": 1, "source": 2, "target": 3}, {"weight": 1, "... | {"states": [2711, 2709], "expectation_value": -0.17782023458083673, "params": [0.49100000000000005, 0.4899, 0.3239, 0.2988, 0.49260000000000004, 0.49710000000000004, 0.2936, 0.2934, 0.4917, 0.4919, 0.2969, 0.2932, 0.3002, 0.29510000000000003, 0.4884, 0.48910000000000003, 0.36660000000000004, 0.36160000000000003, 0.4474... | 0.25 * (Z(0) @ Z(1)) + 0.00034722222222222224 * (Z(2) @ Z(0)) + 0.00034722222222222224 * (Z(3) @ Z(1)) + 0.25 * (Z(3) @ Z(2)) + -0.0010416666666666667 * (Z(4) @ Z(0)) + -0.0015625 * (Z(4) @ Z(2)) + -0.0010416666666666667 * (Z(5) @ Z(1)) + -0.0015625 * (Z(5) @ Z(3)) + 0.25 * (Z(5) @ Z(4)) + 0.0006944444444444445 * (Z(6)... | 13 | 12 | 2 | {"smallest_eigenvalues": [-1.5131944444444438, -1.5131944444444438, -1.5131944444444438, -1.5131944444444438], "number_of_smallest_eigenvalues": 4, "first_excited_energy": -1.5104166666666665, "smallest_bitstrings": ["100101011010", "101010010101", "010101101010", "011010100101"], "largest_eigenvalue": 1.52291666666666... | OPENQASM 3.0;
include "stdgates.inc";
qubit[12] q;
ry(0.8371932544002377) q[0];
rz(0.20858065204347453) q[0];
ry(-0.45655694041749045) q[1];
ry(0.4641984393163029) q[2];
ry(-0.19028136922153194) q[3];
ry(1.019406464640929) q[4];
ry(-0.07467794364198581) q[5];
ry(0.1078744572788903) q[6];
ry(0.5781622452340566) q[7];
ry... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"communities_size": 3, "number_of_communities": 2} | {"circuits": [], "gradients": []} | [
"IIIIIIIIIIZZ",
"IIIIIIIIIZIZ",
"IIIIIIIIZIZI",
"IIIIIIIIZZII",
"IIIIIIIZIIIZ",
"IIIIIIIZIZII",
"IIIIIIZIIIZI",
"IIIIIIZIZIII",
"IIIIIIZZIIII",
"IIIIIZIIIIIZ",
"IIIIIZIIIZII",
"IIIIIZIZIIII",
"IIIIZIIIIIZI",
"IIIIZIIIZIII",
"IIIIZIZIIIII",
"IIIIZZIIIIII",
"IIIZIIIIIIIZ",
"IIIZIIIII... | [
0.25,
0.00034722222222222224,
0.00034722222222222224,
0.25,
-0.0010416666666666667,
-0.0015625,
-0.0010416666666666667,
-0.0015625,
0.25,
0.0006944444444444445,
0.00034722222222222224,
-0.0010416666666666667,
0.0006944444444444445,
0.00034722222222222224,
-0.0010416666666666667,
0.25,
... | 0.97248 | [
0.8371932544002377,
-0.45655694041749045,
0.4641984393163029,
-0.19028136922153194,
1.019406464640929,
-0.07467794364198581,
0.1078744572788903,
0.5781622452340566,
-0.09758270765337963,
0.42316099187094136,
-0.019552344140408177,
0.5019802359551023,
0.41716130408694907,
-0.391375460764549... | {
"n_parameters": 94,
"n_qubits": 12,
"optimal_eigenvalue": -1.5131944444444438,
"target_ratio": 0.97,
"target_value": -1.4677986111111105
} | 23 |
3415806688122177614 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], "hyperedges": [[3, 5, 6], [0, 9, 3], [8, 9, 5], [9, 1], [8, 2], [9, 10, 5], [2, 4, 5], [0, 4], [6, 7], [0, 7], [10, 6], [1, 7], [10, 7], [9, 2], [0, 1, 2], [1, 4, 6], [8, 4, 7], [8, 4, 5], [9, 3, 4], [10, 3, 5], [1, 10], [8, 3, 5]]} | {"states": [1016, 1000], "expectation_value": -5.360727275561041, "params": [-0.0025, 0.9661000000000001, 2.1251, 0.0025, 2.0189, 0.0028, 2.7025, -0.0022, 3.0008000000000004, 0.0034000000000000002, 3.0867, -0.0021000000000000003, 3.0923000000000003, 0.8084, 3.0820000000000003, 1.1386, -0.0019, -0.8873000000000001, -0.0... | 0.5 * (Z(3) @ Z(5)) + 0.16666666666666666 * (Z(6) @ Z(5)) + 0.16666666666666666 * (Z(6) @ Z(3)) + 0.16666666666666666 * (Z(0) @ Z(3)) + 0.3333333333333333 * (Z(9) @ Z(5)) + 0.3333333333333333 * (Z(9) @ Z(3)) + 0.16666666666666666 * (Z(9) @ Z(0)) + 0.5 * (Z(8) @ Z(5)) + 0.16666666666666666 * (Z(8) @ Z(3)) + 0.1666666666... | 4 | 11 | 1 | {"smallest_eigenvalues": [-5.666666666666668], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -5.333333333333334, "smallest_bitstrings": ["10000010111"], "largest_eigenvalue": 17.000000000000004} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
rx(-0.025311091885855355) q[0];
rz(2.684065923308413) q[0];
rx(2.2729810106081896) q[1];
rz(1.5092376419032094) q[1];
rx(1.9672439500624848) q[2];
rz(1.4703737702988455) q[2];
rx(2.7640412826165255) q[3];
rz(1.640214642881051) q[3];
rx(3.1232747766670244) q[4];
rz(1.70... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIZIZIII",
"IIIIZZIIIII",
"IIIIZIIZIII",
"IIIIIIIZIIZ",
"IZIIIZIIIII",
"IZIIIIIZIII",
"IZIIIIIIIIZ",
"IIZIIZIIIII",
"IIZIIIIZIII",
"IZZIIIIIIII",
"IIIIZIIIIZI",
"IIIIIIIIIZZ",
"IZIIIIIIIZI",
"IIIIIZIIZII",
"IIIIIIIIZIZ",
"IZIIIIIIZII",
"IIZIIIIIZII",
"IIIIIIIIZZI",
"ZIIIIZIII... | [
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.3333333333333333,
0.3333333333333333,
0.16666666666666666,
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.16666666666666666,
0.16666666666666666,
0.5,
0.5,
0.16666... | 0.972519 | [
-0.025311091885855355,
1.1132695965135166,
2.2729810106081896,
-0.06155868489168712,
1.967243950062485,
-0.10042255649605059,
2.7640412826165255,
0.06941831608615459,
3.1232747766670244,
0.13709027390772374,
3.125480613894318,
0.12843077506961248,
3.4427619552245634,
0.9008052932222,
3.0... | {
"n_parameters": 31,
"n_qubits": 11,
"optimal_eigenvalue": -5.666666666666668,
"target_ratio": 0.97,
"target_value": -5.496666666666668
} | 5 |
1e92ea5f7cae37ca987f17ac92d103da | connected_components | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}, {"id": 10}, {"id": 11}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 1, "target": 2},... | {"states": [15, 127], "expectation_value": -2.7407410119052424, "params": [[-0.0766], [0.0702]], "bitstrings": ["11111110000", "11110000000"], "total_optimization_steps": 10, "probabilities": [0.001255672313871284, 0.0013225465458685378], "optimization_time": 3.4254939556121826} | -2.5 * (Z(0) @ Z(1)) + -2.5 * (Z(2) @ Z(1)) + -2.5 * (Z(2) @ Z(0)) + -2.5 * (Z(3) @ Z(1)) + -2.5 * (Z(3) @ Z(0)) + -2.5 * (Z(3) @ Z(2)) + -1.5 * (Z(4) @ Z(5)) + -1.5 * (Z(6) @ Z(5)) + -1.5 * (Z(6) @ Z(4)) + -2.0 * (Z(7) @ Z(8)) + 1.0 * (Z(9) @ Z(8)) + -2.0 * (Z(9) @ Z(7)) + -2.0 * (Z(10) @ Z(8)) + -2.0 * (Z(10) @ Z(7))... | 1 | 11 | 1 | {"smallest_eigenvalues": [-36.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -33.0, "smallest_bitstrings": ["11110000000"], "largest_eigenvalue": 18.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(-1.10965568731028e-08) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(-1.10965568731028e-08) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(-1.10965568731028e-08) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(-1.10965568731028e-08) q[3];
cx q... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
bit[11] c;
qubit[11] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
h q[8];
h q[9];
h q[10];
cx q[1], q[0];
rz(x0) q[0];
c... | {"node": 2} | {"circuits": [], "gradients": []} | [
"IIIIIIIIIZZ",
"IIIIIIIIZZI",
"IIIIIIIIZIZ",
"IIIIIIIZIZI",
"IIIIIIIZIIZ",
"IIIIIIIZZII",
"IIIIIZZIIII",
"IIIIZZIIIII",
"IIIIZIZIIII",
"IIZZIIIIIII",
"IZZIIIIIIII",
"IZIZIIIIIII",
"ZIZIIIIIIII",
"ZIIZIIIIIII",
"ZZIIIIIIIII",
"IIIIIIIIIZI",
"IIIIIIIIIIZ",
"IIIIIIIIZII",
"IIIIIIIZI... | [
-2.5,
-2.5,
-2.5,
-2.5,
-2.5,
-2.5,
-1.5,
-1.5,
-1.5,
-2,
1,
-2,
-2,
-2,
-2,
-2,
2,
-2,
-2,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5
] | 0.944444 | [
-1.10965568731028e-8,
3.1415926601612125,
1.570796325451994,
1.570796275059673,
1.5707963454780094,
-1.5707962934871835,
1.5707963184710743
] | {
"n_parameters": 7,
"n_qubits": 11,
"optimal_eigenvalue": -36,
"target_ratio": 0.97,
"target_value": -34.92
} | 201 |
cacbe081b77503da3f10c68300c494cc | vertex_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 6}, {"source": 0, "target": 7}, {"source": 1, "target": 6}, {"source": 2, "target": 3}, {"source": 2, "target": 4}, {"source": 2, "ta... | {"states": [28, 220], "expectation_value": -5.064056116190093, "params": [1.4027, 0.0036000000000000003, 1.4147, 0.0035, 1.3998000000000002, 0.0009000000000000001, 1.4034, -0.0009000000000000001, 1.4088, -0.0035, 1.4152, -0.0051, -0.0007, -0.0066, -0.006, 0.004, 1.3971, 1.3857000000000002, -1.3895, 1.389, 1.3931, -1.34... | 0.5 * (Z(0) @ Z(6)) + 0.5 * (Z(7) @ Z(6)) + 0.5 * (Z(7) @ Z(0)) + 0.5 * (Z(1) @ Z(6)) + 0.5 * (Z(2) @ Z(7)) + 0.5 * (Z(3) @ Z(7)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(4) @ Z(6)) + 0.5 * (Z(4) @ Z(2)) + 0.5 * (Z(5) @ Z(6)) + 0.5 * (Z(5) @ Z(7)) + 0.5 * (Z(5) @ Z(2)) + -2.0 * Z(6) + -0.5 * Z(0) + -2.0 * Z(7) + 0.0 * Z(1) + -... | 4 | 8 | 1 | {"smallest_eigenvalues": [-7.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -6.0, "smallest_bitstrings": ["00100011"], "largest_eigenvalue": 14.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rx(2.09196604600786) q[0];
rz(1.5574065964741761) q[0];
rx(2.8819335098396586) q[1];
rz(1.8778812525993054) q[1];
rx(1.6877852575138939) q[2];
rz(1.4466203607817718) q[2];
rx(1.7060787709357488) q[3];
rz(1.4518287150750506) q[3];
rx(1.9858897888732088) q[4];
rz(2.020013... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IZIIIIIZ",
"ZZIIIIII",
"ZIIIIIIZ",
"IZIIIIZI",
"ZIIIIZII",
"ZIIIZIII",
"IIIIZZII",
"IZIZIIII",
"IIIZIZII",
"IZZIIIII",
"ZIZIIIII",
"IIZIIZII",
"IZIIIIII",
"IIIIIIIZ",
"ZIIIIIII",
"IIIIIIZI",
"IIIIIZII",
"IIIIZIII",
"IIIZIIII",
"IIZIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-2,
-0.5,
-2,
0,
-1.5,
-0.5,
-0.5,
-1
] | 0.976893 | [
2.09196604600786,
-0.013389730320720411,
2.8819335098396586,
0.30708492580440894,
1.687785257513894,
-0.1241759660131244,
1.7060787709357488,
-0.11896761171984598,
1.9858897888732088,
0.44921682329589974,
3.2748315763454308,
0.28630842724256855,
-0.05017701126291544,
-0.3145922534704872,
... | {
"n_parameters": 23,
"n_qubits": 8,
"optimal_eigenvalue": -7,
"target_ratio": 0.97,
"target_value": -6.79
} | 21 |
6998245398537875737 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7], "hyperedges": [[2, 3, 7], [0, 3, 4, 5], [1, 5, 7], [1, 2, 5, 6], [0, 1, 2, 4, 6, 7], [1, 2, 3, 4, 5]]} | {"states": [219, 175], "expectation_value": -0.789922625824052, "params": [[-0.4096], [0.40800000000000003]], "bitstrings": ["00100100", "01010000"], "total_optimization_steps": 50, "probabilities": [0.0098365750362365, 0.010156835329450093], "optimization_time": 2.4257678985595703} | 0.21666666666666667 * (Z(2) @ Z(3)) + 0.16666666666666666 * (Z(7) @ Z(3)) + 0.19999999999999998 * (Z(7) @ Z(2)) + 0.08333333333333333 * (Z(0) @ Z(3)) + 0.03333333333333333 * (Z(0) @ Z(2)) + 0.03333333333333333 * (Z(0) @ Z(7)) + 0.13333333333333333 * (Z(4) @ Z(3)) + 0.08333333333333334 * (Z(4) @ Z(2)) + 0.03333333333333... | 1 | 8 | 1 | {"smallest_eigenvalues": [-1.533333333333333], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -1.4833333333333332, "smallest_bitstrings": ["01010000"], "largest_eigenvalue": 6.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
cx q[3], q[2];
rz(-5.135582602057772e-08) q[2];
cx q[3], q[2];
h q[4];
h q[5];
h q[6];
h q[7];
cx q[3], q[7];
rz(2.561862492604449e-08) q[7];
cx q[3], q[7];
cx q[2], q[7];
cx q[3], q[0];
rz(1.2204412241250852e-08) q[0];
cx q[3], q[0];
cx ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] ... | null | {"circuits": [], "gradients": []} | [
"IIIIZZII",
"ZIIIZIII",
"ZIIIIZII",
"IIIIZIIZ",
"IIIIIZIZ",
"ZIIIIIIZ",
"IIIZZIII",
"IIIZIZII",
"ZIIZIIII",
"IIIZIIIZ",
"IIZIZIII",
"IIZIIZII",
"ZIZIIIII",
"IIZIIIIZ",
"IIZZIIII",
"IIIIZIZI",
"IIIIIZZI",
"ZIIIIIZI",
"IIIIIIZZ",
"IIIZIIZI",
"IIZIIIZI",
"IZIIIZII",
"ZZIIIII... | [
0.21666666666666667,
0.16666666666666666,
0.19999999999999998,
0.08333333333333333,
0.03333333333333333,
0.03333333333333333,
0.13333333333333333,
0.08333333333333334,
0.03333333333333333,
0.11666666666666667,
0.13333333333333333,
0.13333333333333333,
0.16666666666666666,
0.083333333333333... | 0.858696 | [
-5.135582602057772e-8,
2.561862492604449e-8,
-6.835839047987414e-8,
1.2204412241250852e-8,
9.966606881568994e-10,
3.858197456100111e-9,
1.158419106995561e-7,
1.2794364248122165e-7,
1.2116717248400008e-7,
-1.5707962849490553,
-1.5707961191926691,
1.5707963730149037,
-1.57079559192981,
1.570... | {
"n_parameters": 16,
"n_qubits": 8,
"optimal_eigenvalue": -1.533333333333333,
"target_ratio": 0.97,
"target_value": -1.487333333333333
} | 378 |
-5195831292867703356 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6], "hyperedges": [[3, 4], [2, 4], [1, 5], [2, 3, 5], [5, 6], [0, 3]]} | {"states": [70, 57], "expectation_value": -0.01596034018113473, "params": [[-0.038200000000000005], [0.038200000000000005]], "bitstrings": ["0111001", "1000110"], "total_optimization_steps": 10, "probabilities": [0.008048751349393441, 0.008064392385747054], "optimization_time": 1.4532430171966553} | 0.5 * (Z(3) @ Z(4)) + 0.5 * (Z(2) @ Z(4)) + 0.16666666666666666 * (Z(2) @ Z(3)) + 0.16666666666666666 * (Z(5) @ Z(3)) + 0.16666666666666666 * (Z(5) @ Z(2)) + 0.5 * (Z(1) @ Z(5)) + 0.5 * (Z(6) @ Z(5)) + 0.5 * (Z(0) @ Z(3)) + 0.0 * Z(4) + 0.16666666666666674 * Z(3) + 0.16666666666666663 * Z(2) + 0.16666666666666674 * Z(5... | 1 | 7 | 1 | {"smallest_eigenvalues": [-2.833333333333334], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.5, "smallest_bitstrings": ["1000110"], "largest_eigenvalue": 3.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
cx q[4], q[3];
rz(-0.9745053982371106) q[3];
cx q[4], q[3];
cx q[4], q[2];
rz(-0.9745053982371106) q[2];
cx q[4], q[2];
cx q[3], q[2];
rz(-0.013980265919903884) q[2];
cx q[3], q[2];
rz(0.010306916410358191) q[4];
rx(0.773785440580... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
bit[7] c;
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[4], q[3];
rz(x0) q[3];
cx q[4], q[3];
cx q[4], q[2];
rz(x0) q[2];
cx q[4], q[2];
cx q[3], q[2];
rz(x1) q[2];
cx q[3], q... | null | {"circuits": [], "gradients": []} | [
"IIZZIII",
"IIZIZII",
"IIIZZII",
"IZIZIII",
"IZIIZII",
"IZIIIZI",
"ZZIIIII",
"IIIZIIZ",
"IIZIIII",
"IIIZIII",
"IIIIZII",
"IZIIIII",
"IIIIIZI",
"ZIIIIII",
"IIIIIIZ"
] | [
0.5,
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.5,
0.5,
0,
0.16666666666666674,
0.16666666666666663,
0.16666666666666674,
0,
0,
0
] | 0.526894 | [
-0.9745053982371106,
-0.013980265919903884,
0.0103069164103583,
0.7737854405808111
] | {
"n_parameters": 4,
"n_qubits": 7,
"optimal_eigenvalue": -2.833333333333334,
"target_ratio": 0.97,
"target_value": -2.748333333333334
} | 115 |
90cd45aecbe758daa031a854118281c7 | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 4}, {"source": 1, "target": 2}, {"source": 1, "target": 4}, {"source": 2, "target": 3}, {"source": 2, "target": 4}, {"source": 3, "target": 4}, ... | {"states": [114, 122], "expectation_value": -1.4097269820096372, "params": [0.0022, -0.5321, 0.5717, 0.4801, 0.8025, 0.27890000000000004, 0.8031, 0.010100000000000001, 0.8068000000000001, 0.0026000000000000003, 0.8036000000000001, 0.0049, 0.0022, 0.6001000000000001, 0.8011, 0.4612, 0.7977000000000001, 0.3111, 0.0022, 0... | 0.5 * (Z(1) @ Z(2)) + 0.25 * (Z(3) @ Z(1)) + 0.25 * (Z(4) @ Z(1)) + 0.25 * (Z(3) @ Z(4)) + -0.25 * (Z(3) @ Z(4) @ Z(1)) + 0.125 * (Z(3) @ Z(5)) + 0.125 * (Z(3) @ Z(6)) + 0.125 * (Z(3) @ Z(7)) + 0.125 * (Z(5) @ Z(6)) + 0.125 * (Z(5) @ Z(7)) + 0.125 * (Z(6) @ Z(7)) + -0.125 * (Z(3) @ Z(5) @ Z(6)) + -0.125 * (Z(3) @ Z(5) ... | 18 | 9 | 2 | {"smallest_eigenvalues": [-3.9375, -3.9375], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -2.9375, "smallest_bitstrings": ["110000110", "110000101"], "largest_eigenvalue": 6.0625} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(0.056912986577473866) q[0];
rz(0.3094642138848882) q[0];
rx(-0.155076333841582) q[1];
rz(0.3052202151005613) q[1];
rx(0.8584301783604933) q[2];
rz(0.08129913585944087) q[2];
rx(1.1489608051634745) q[3];
rz(-0.23794780314121378) q[3];
rx(0.6604106178284125) q[4];
rz(-... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZZI",
"IIIIIZIZI",
"IIIIZIIZI",
"IIIIZZIII",
"IIIIZZIZI",
"IIIZIZIII",
"IIZIIZIII",
"IZIIIZIII",
"IIZZIIIII",
"IZIZIIIII",
"IZZIIIIII",
"IIZZIZIII",
"IZIZIZIII",
"IZZIIZIII",
"IZZZIIIII",
"IZZZIZIII",
"IIIIIIZIZ",
"IIIIZIIIZ",
"IIIZIIIIZ",
"ZIIIIIIIZ",
"IIIIZIZII",
"... | [
0.5,
0.25,
0.25,
0.25,
-0.25,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625... | 0.975467 | [
0.05691298657747386,
0.5132692831194525,
-0.155076333841582,
0.3052202151005613,
0.8584301783604933,
0.08129913585944087,
1.1489608051634745,
-0.23794780314121378,
0.6604106178284125,
-0.031076673860656233,
0.9177511790288277,
0.32405280952797977,
0.22133575689637358,
0.16741808596700913,
... | {
"n_parameters": 99,
"n_qubits": 9,
"optimal_eigenvalue": -3.9375,
"target_ratio": 0.97,
"target_value": -3.819375
} | 36 |
c481e42d7da0b37a314b8b7c8726899d | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 1, "id": 3}, {"bipartite": 1, "id": 4}, {"bipartite": 1, "id": 5}, {"bipartite": 1, "id": 6}, {"bipartite": 1, "id": 7}, {"bipartite": 1, "id": 8}], "edges": [{"... | {"states": [95, 91], "expectation_value": -58.73721512469042, "params": [-0.0019, 0.9827, 1.4979, 0.2546, 0.5998, 0.5477000000000001, 1.4986000000000002, 0.0424, 1.4939, -0.16920000000000002, 0.7445, -0.35150000000000003, 1.488, -0.12810000000000002, 1.488, 0.0114, -0.0019, 0.009000000000000001, 1.4973, 0.0046, 0.60330... | 5.0 * (Z(0) @ Z(1)) + 5.0 * (Z(2) @ Z(1)) + 5.0 * (Z(3) @ Z(2)) + 5.0 * (Z(4) @ Z(1)) + 5.0 * (Z(4) @ Z(2)) + 5.0 * (Z(5) @ Z(4)) + 5.0 * (Z(6) @ Z(3)) + 5.0 * (Z(6) @ Z(4)) + 5.0 * (Z(6) @ Z(5)) + 5.0 * (Z(7) @ Z(4)) + 5.0 * (Z(7) @ Z(5)) + 5.0 * (Z(7) @ Z(6)) + 11.5 * Z(1) + -3.5 * Z(0) + 7.0 * Z(2) + 9.5 * Z(3) + 21... | 18 | 8 | 2 | {"smallest_eigenvalues": [-68.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -63.5, "smallest_bitstrings": ["10100100"], "largest_eigenvalue": 143.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rx(0.027092942245099942) q[0];
rz(1.4300677455331456) q[0];
rx(1.5730024856267992) q[1];
rz(0.20492604183086316) q[1];
rx(-0.023114436645791478) q[2];
rz(0.49352247579539243) q[2];
rx(1.618738856137882) q[3];
rz(-0.03986295434416167) q[3];
rx(1.5780662223481097) q[4];
r... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum_bipartite", "extra": "{\"left_nodes\": [0, 1, 2], \"right_nodes\": [3, 4, 5, 6, 7, 8]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZZI",
"IIIIZZII",
"IIIZIIZI",
"IIIZIZII",
"IIZZIIII",
"IZIIZIII",
"IZIZIIII",
"IZZIIIII",
"ZIIZIIII",
"ZIZIIIII",
"ZZIIIIII",
"IIIIIIZI",
"IIIIIIIZ",
"IIIIIZII",
"IIIIZIII",
"IIIZIIII",
"IIZIIIII",
"IZIIIIII",
"ZIIIIIII"
] | [
5,
5,
5,
5,
5,
5,
5,
5,
5,
5,
5,
5,
11.5,
-3.5,
7,
9.5,
21.5,
9,
17,
11.5
] | 0.980721 | [
0.027092942245099942,
1.1930698625248446,
1.5730024856267992,
0.20492604183086316,
-0.023114436645791478,
0.49352247579539243,
1.618738856137882,
-0.03986295434416167,
1.5780662223481097,
-0.2963538964804383,
0.23108841805420396,
-0.6399705658938811,
1.3614370865277474,
-0.0266465158994803... | {
"n_parameters": 42,
"n_qubits": 8,
"optimal_eigenvalue": -68.5,
"target_ratio": 0.97,
"target_value": -66.445
} | 10 |
-7216443839465865534 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4], "hyperedges": [[2, 3, 4], [0, 1, 3], [1, 4]]} | {"states": [30, 14], "expectation_value": -0.801152681741158, "params": [[[1.5577, 0.0046], [2.6701, 0.0012000000000000001], [2.9005, 0.0014], [2.9025000000000003, 0.005200000000000001], [0.6851, 0.0026000000000000003]]], "bitstrings": ["00001", "10001"], "total_optimization_steps": 290, "probabilities": [0.40211095498... | 0.16666666666666666 * (Z(2) @ Z(3)) + 0.16666666666666666 * (Z(4) @ Z(3)) + 0.16666666666666666 * (Z(4) @ Z(2)) + 0.16666666666666666 * (Z(0) @ Z(3)) + 0.16666666666666666 * (Z(1) @ Z(3)) + 0.5 * (Z(1) @ Z(4)) + 0.16666666666666666 * (Z(1) @ Z(0)) + 0.3333333333333333 * Z(3) + 0.16666666666666666 * Z(2) + 0.16666666666... | 1 | 5 | 1 | {"smallest_eigenvalues": [-1.1666666666666665, -1.1666666666666665], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -0.8333333333333333, "smallest_bitstrings": ["10001", "01100"], "largest_eigenvalue": 2.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[5] q;
rx(-0.057183093902666515) q[0];
rz(1.1972775330389647) q[0];
rx(3.1240121237138307) q[1];
rz(-0.43232359775380136) q[1];
rx(3.3591548222345597) q[2];
rz(0.6997024399260359) q[2];
rx(3.3616474180205063) q[3];
rz(0.4636078135785392) q[3];
rx(-0.10334144256672051) q[4];
rz... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
input float[64] x9;
bit[5] c;
qubit[5] q;
rx(x0) q[0];
rz(x1) q[0];
rx(x2) q[1];
rz(x3) q[1];
rx(x4) q... | null | {"circuits": [], "gradients": []} | [
"IZZII",
"ZZIII",
"ZIZII",
"IZIIZ",
"IZIZI",
"ZIIZI",
"IIIZZ",
"IZIII",
"IIZII",
"ZIIII",
"IIIIZ",
"IIIZI"
] | [
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.16666666666666666,
0.3333333333333333,
0.16666666666666666,
0.16666666666666663,
0.16666666666666666,
0.16666666666666663
] | 0.986333 | [
-0.057183093902666515,
1.1972775330389647,
3.1240121237138307,
-0.43232359775380136,
3.3591548222345597,
0.6997024399260359,
3.3616474180205063,
0.4636078135785392,
-0.10334144256672051,
-0.1617044047495809
] | {
"n_parameters": 10,
"n_qubits": 5,
"optimal_eigenvalue": -1.1666666666666665,
"target_ratio": 0.97,
"target_value": -1.1316666666666666
} | 10 |
cba3c0f3028bedd24c97c562399fe60f | kclique | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 5}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, ... | {"states": [13, 7], "expectation_value": -2.594076482325791, "params": [[-0.0472], [0.056600000000000004]], "bitstrings": ["1110010", "1111000"], "total_optimization_steps": 10, "probabilities": [0.009566880240389007, 0.009925817282944645], "optimization_time": 2.4979491233825684} | 2.25 * (Z(0) @ Z(1)) + 2.25 * (Z(2) @ Z(1)) + 2.25 * (Z(2) @ Z(0)) + 2.25 * (Z(3) @ Z(1)) + 2.25 * (Z(3) @ Z(0)) + 2.25 * (Z(3) @ Z(2)) + 2.5 * (Z(4) @ Z(1)) + 2.5 * (Z(4) @ Z(0)) + 2.5 * (Z(4) @ Z(2)) + 2.5 * (Z(4) @ Z(3)) + 2.5 * (Z(5) @ Z(1)) + 2.25 * (Z(5) @ Z(0)) + 2.5 * (Z(5) @ Z(2)) + 2.5 * (Z(5) @ Z(3)) + 2.25 ... | 1 | 7 | 1 | {"smallest_eigenvalues": [-13.75], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -11.75, "smallest_bitstrings": ["1111000"], "largest_eigenvalue": 72.25} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(-4.011935460582535e-09) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(-4.011935460582535e-09) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(-4.011935460582535e-09) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(-4.011935460582535e-09) q[3];
c... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
bit[7] c;
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[1], q[0];
rz(x0) q[0];
cx q[1], q[0];
cx q[1], q[2];
rz(x0) q[2];
cx q[1], q[2]... | {"k": 4} | {"circuits": [], "gradients": []} | [
"IIIIIZZ",
"IIIIZZI",
"IIIIZIZ",
"IIIZIZI",
"IIIZIIZ",
"IIIZZII",
"IIZIIZI",
"IIZIIIZ",
"IIZIZII",
"IIZZIII",
"IZIIIZI",
"IZIIIIZ",
"IZIIZII",
"IZIZIII",
"IZZIIII",
"ZIIIIZI",
"ZIIIIIZ",
"ZIIIZII",
"ZIIZIII",
"ZIZIIII",
"ZZIIIII",
"IIIIIZI",
"IIIIIIZ",
"IIIIZII",
"III... | [
2.25,
2.25,
2.25,
2.25,
2.25,
2.25,
2.5,
2.5,
2.5,
2.5,
2.5,
2.25,
2.5,
2.5,
2.25,
2.5,
2.5,
2.5,
2.5,
2.5,
2.25,
-3.25,
-3.5,
-3.25,
-3.25,
-2.75,
-3.25,
-2.75
] | 0.740989 | [
-4.011935460582535e-9,
1.3554674035363465e-8,
0.9694266146810376,
1.5707964080681434,
-1.5707962967130897,
1.5707963408013987
] | {
"n_parameters": 6,
"n_qubits": 7,
"optimal_eigenvalue": -13.75,
"target_ratio": 0.97,
"target_value": -13.3375
} | 195 |
eba59f50c284ea491834da7e16fa8fc7 | vertex_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 3}, {"source": 0, "target": 6}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 1, "target": 6}, {"source": 2, "ta... | {"states": [133, 197], "expectation_value": -4.219550323308187, "params": [0.39780000000000004, 0.0032, 0.3906, 0.0031000000000000003, 0.2582, -0.0177, 0.2516, -0.016, 0.0001, 0.2323, -0.0047, 0.2569, -0.0008, 0.24130000000000001, 0.0008, 0.24230000000000002, 0.010400000000000001, 0.2519, 0.0102, 0.2782, 0.391800000000... | 0.5 * (Z(0) @ Z(3)) + 0.5 * (Z(6) @ Z(0)) + 0.5 * (Z(1) @ Z(3)) + 0.5 * (Z(1) @ Z(6)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(7) @ Z(6)) + 0.5 * (Z(7) @ Z(2)) + 0.5 * (Z(4) @ Z(3)) + 0.5 * (Z(5) @ Z(4)) + -1.0 * Z(3) + -0.5 * Z(0) + -1.0 * Z(6) + -1.0 * Z(1) + -0.5 * Z(2) + -0.5 * Z(7) + -0.5 * Z(4) + 0.0 * Z(5) | 7 | 8 | 4 | {"smallest_eigenvalues": [-4.5, -4.5, -4.5], "number_of_smallest_eigenvalues": 3, "first_excited_energy": -3.5, "smallest_bitstrings": ["00110110", "11001001", "00111010"], "largest_eigenvalue": 9.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rx(0.38052690791396165) q[0];
rz(0.12876224261210822) q[0];
rx(0.4129431632583738) q[1];
rz(-0.06465084134299584) q[1];
cx q[1], q[0];
rz(-0.16858860617837823) q[0];
cx q[1], q[0];
rz(1.5592973732717885) q[0];
ry(0.7000341781004477) q[0];
rz(-1.6857574732511131) q[0];
r... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x100;
input float[64] x101;
input float[64] x102;
input float[64] x103;
input float[64] x104;
input float[64] x105;
input float[64] x106;
input float[64] x107;
input float[64] x108;
input float[64] x109;
i... | null | {"circuits": [], "gradients": []} | [
"IIIIZIIZ",
"IZIIIIIZ",
"IIIIZIZI",
"IZIIIIZI",
"IIIIIZZI",
"ZZIIIIII",
"ZIIIIZII",
"IIIZZIII",
"IIZZIIII",
"IIIIZIII",
"IIIIIIIZ",
"IZIIIIII",
"IIIIIIZI",
"IIIIIZII",
"ZIIIIIII",
"IIIZIIII",
"IIZIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1,
-0.5,
-1,
-1,
-0.5,
-0.5,
-0.5,
0
] | 0.971281 | [
0.3805269079139617,
-0.039826363566269986,
0.4129431632583738,
-0.06465084134299584,
0.0026392553186233812,
0.17111628982817592,
0.16301495096394006,
0.10067041393419487,
0.02266213442633431,
0.1936882971656938,
0.45767754317687187,
0.07251452325467028,
-0.001591014420485962,
0.27170146128... | {
"n_parameters": 144,
"n_qubits": 8,
"optimal_eigenvalue": -4.5,
"target_ratio": 0.97,
"target_value": -4.365
} | 3 |
e4f5057259aaeddd1dd7f4f1ea49da8b | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"capacity": 5, "source": 0, "target": 3}, {"capacity": 6, "source": 0, "target": 4}, {"capacity": 5, "source": 0, "target": 5}, {"capacity": 3, "source": 1, ... | {"states": [65, 1], "expectation_value": -1.7668843163247625, "params": [[-0.054700000000000006, -0.008700000000000001], [0.06720000000000001, 0.032]], "bitstrings": ["10111110", "11111110"], "total_optimization_steps": 10, "probabilities": [0.006797623887878825, 0.006998452372276537], "optimization_time": 6.6032252311... | -1.25 * (Z(0) @ Z(3)) + -1.5 * (Z(4) @ Z(0)) + -1.25 * (Z(5) @ Z(0)) + -0.25 * (Z(5) @ Z(4)) + -0.5 * (Z(6) @ Z(3)) + -1.0 * (Z(6) @ Z(4)) + -0.75 * (Z(1) @ Z(6)) + -1.5 * (Z(2) @ Z(3)) + -1.0 * (Z(2) @ Z(4)) + -0.75 * (Z(7) @ Z(3)) + 4.25 * (Z(7) @ Z(0)) + 1.5 * Z(3) + -0.25 * Z(0) + -3.25 * Z(4) + -1.5 * Z(5) + -0.25... | 1 | 8 | 2 | {"smallest_eigenvalues": [-19.5, -19.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -17.5, "smallest_bitstrings": ["11111110", "10111110"], "largest_eigenvalue": 18.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
cx q[3], q[0];
rz(0.022546435908237288) q[0];
cx q[3], q[0];
h q[4];
cx q[0], q[4];
rz(0.14518918596484848) q[4];
cx q[0], q[4];
h q[5];
cx q[0], q[5];
rz(0.022546435908237288) q[5];
cx q[0], q[5];
cx q[4], q[5];
rz(0.7517255380687702) q[... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"source": 0, "sink": 7} | {"circuits": [], "gradients": []} | [
"IIIIZIIZ",
"IIIZIIIZ",
"IIZIIIIZ",
"IIZZIIII",
"IZIIZIII",
"IZIZIIII",
"IZIIIIZI",
"IIIIZZII",
"IIIZIZII",
"ZIIIZIII",
"ZIIIIIIZ",
"IIIIZIII",
"IIIIIIIZ",
"IIIZIIII",
"IIZIIIII",
"IZIIIIII",
"IIIIIIZI",
"IIIIIZII",
"ZIIIIIII"
] | [
-1.25,
-1.5,
-1.25,
-0.25,
-0.5,
-1,
-0.75,
-1.5,
-1,
-0.75,
4.25,
1.5,
-0.25,
-3.25,
-1.5,
-0.25,
0.75,
-0.5,
3.5
] | 0.957735 | [
0.022546435908237288,
0.14518918596484848,
0.7517255380687702,
0.6453322187153919,
0.0005547510135491637,
0.01648942695497035,
-0.24567836598873122,
0.7103534844820352,
1.2276522599760762,
-0.7579580526703535,
-0.6595794244215516,
1.6514152238781217,
0.05475463053088248,
0.2385240506869008... | {
"n_parameters": 24,
"n_qubits": 8,
"optimal_eigenvalue": -19.5,
"target_ratio": 0.97,
"target_value": -18.915
} | 500 |
d65950f441381bc87796af7b1ba14020 | connected_components | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}, {"id": 10}, {"id": 11}, {"id": 12}, {"id": 13}, {"id": 14}], "edges": [{"source": 0, "target": 1}, {"source": 2, "target": 3}, {"source": 2, "targ... | {"states": [16263, 16319], "expectation_value": -14.408799376513452, "params": [-0.0039000000000000003, 0.0016, 2.7928, -0.0034000000000000002, 0.0021000000000000003, 0.4015, -1.5444, -0.0019, -1.4764000000000002, -0.0033, 0.060500000000000005, 0.0026000000000000003, 2.8321, -0.0, -0.0023, 0.30770000000000003, 0.718200... | -1.0 * (Z(0) @ Z(1)) + -1.5 * (Z(2) @ Z(3)) + 0.5 * (Z(4) @ Z(3)) + -1.5 * (Z(4) @ Z(2)) + -1.0 * (Z(5) @ Z(6)) + -1.5 * (Z(8) @ Z(10)) + -1.5 * (Z(9) @ Z(10)) + 0.5 * (Z(9) @ Z(8)) + -1.5 * (Z(11) @ Z(12)) + -1.5 * (Z(13) @ Z(12)) + 0.5 * (Z(13) @ Z(11)) + 0.5 * Z(1) + 0.5 * Z(0) + 0.5 * Z(3) + 0.5 * Z(2) + 0.5 * Z(4)... | 4 | 14 | 1 | {"smallest_eigenvalues": [-16.499999999999904], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -15.499999999999917, "smallest_bitstrings": ["00000001000000"], "largest_eigenvalue": 14.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[14] q;
rx(0.07833200733441541) q[0];
rz(1.4890772580790603) q[0];
rx(2.74114002951368) q[1];
rz(1.78670250739893) q[1];
rx(0.046235595030898836) q[2];
rz(2.2517071069930736) q[2];
rx(-1.5826329063664206) q[3];
rz(1.6986364478023663) q[3];
rx(-1.3729992906077069) q[4];
rz(1.48... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"node": 7} | {"circuits": [], "gradients": []} | [
"IIIIIIIIIIIIZZ",
"IIIIIIIIIIZZII",
"IIIIIIIIIZZIII",
"IIIIIIIIIZIZII",
"IIIIIIIZZIIIII",
"IIIZIZIIIIIIII",
"IIIZZIIIIIIIII",
"IIIIZZIIIIIIII",
"IZZIIIIIIIIIII",
"ZZIIIIIIIIIIII",
"ZIZIIIIIIIIIII",
"IIIIIIIIIIIIZI",
"IIIIIIIIIIIIIZ",
"IIIIIIIIIIZIII",
"IIIIIIIIIIIZII",
"IIIIIIIIIZIIII"... | [
-1,
-1.5,
0.5,
-1.5,
-1,
-1.5,
-1.5,
0.5,
-1.5,
-1.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-0.5
] | 0.97103 | [
0.07833200733441538,
-0.08171906871583642,
2.74114002951368,
0.21590618060403333,
0.04623559503089883,
0.6809107801981773,
-1.5826329063664206,
0.1278401210074699,
-1.3729992906077069,
-0.08101192944268401,
-0.08339565661208866,
0.1773122384121386,
3.076162199260044,
0.5275724214787763,
... | {
"n_parameters": 41,
"n_qubits": 14,
"optimal_eigenvalue": -16.499999999999904,
"target_ratio": 0.97,
"target_value": -16.004999999999907
} | 12 |
40ef9703de0f0e767127b58189c71b80 | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 5}, {"source": 0, "target": 7}, {"source": 1, "target": 2}, {"source": 1, "target": 4}, {"source": 2, "ta... | {"states": [1649, 1653], "expectation_value": -3.837490518328355, "params": [[[1.5858, 0.0034000000000000002], [1.3352000000000002, -0.0009000000000000001], [-0.0035, -0.7754000000000001], [-0.0035, -0.8147000000000001], [1.5876000000000001, 0.0022], [1.5834000000000001, 0.0032], [1.5863, -0.0034000000000000002], [0.28... | 0.25 * (Z(0) @ Z(1)) + 0.25 * (Z(2) @ Z(0)) + 0.25 * (Z(2) @ Z(1)) + -0.25 * (Z(2) @ Z(0) @ Z(1)) + 0.5 * (Z(3) @ Z(4)) + 0.125 * (Z(0) @ Z(3)) + 0.125 * (Z(5) @ Z(0)) + 0.125 * (Z(0) @ Z(6)) + 0.125 * (Z(5) @ Z(3)) + 0.125 * (Z(3) @ Z(6)) + 0.125 * (Z(5) @ Z(6)) + -0.125 * (Z(5) @ Z(0) @ Z(3)) + -0.125 * (Z(0) @ Z(3) ... | 1 | 11 | 2 | {"smallest_eigenvalues": [-4.5, -4.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -3.5, "smallest_bitstrings": ["00110001010", "01010000110"], "largest_eigenvalue": 7.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
rz(-2.14299951443941) q[0];
ry(2.951852322914151) q[0];
rz(0.9480564111784915) q[0];
rz(1.9488952446393757) q[1];
ry(2.9932226655683327) q[1];
rz(-1.016284272532193) q[1];
rz(-1.7088667671243525) q[2];
ry(0.053351181700236616) q[2];
rz(1.1817402719387315) q[2];
rz(-2.3... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIIIZZ",
"IIIIIIIIZIZ",
"IIIIIIIIZZI",
"IIIIIIIIZZZ",
"IIIIIIZZIII",
"IIIIIIIZIIZ",
"IIIIIZIIIIZ",
"IIIIZIIIIIZ",
"IIIIIZIZIII",
"IIIIZIIZIII",
"IIIIZZIIIII",
"IIIIIZIZIIZ",
"IIIIZIIZIIZ",
"IIIIZZIIIIZ",
"IIIIZZIZIII",
"IIIIZZIZIIZ",
"IIIZIZIIIII",
"IIZIIZIIIII",
"IIZZIIIII... | [
0.25,
0.25,
0.25,
-0.25,
0.5,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.25,
0.25,
0.25,
-0.25,
0.5,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.25,
0.25,
0.25,
-0.25,... | 0.985467 | [
1.586356220253404,
0.10337474285472067,
1.3921729469097148,
0.0546427428966528,
-0.04133221330319555,
-0.5675803014114729,
-0.9611966783195071,
1.5689529638212285,
0.08404637766294101,
1.6726427739606242,
0.17612018658686548,
1.5124795154683752,
-0.04757033533011033,
-0.0001558984275410180... | {
"n_parameters": 39,
"n_qubits": 11,
"optimal_eigenvalue": -4.5,
"target_ratio": 0.97,
"target_value": -4.365
} | 8 |
833c89e8aca800e5707fb47ea63f9088 | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"source": 0, "target": 1}, {"source": 1, "target": 4}, {"source": 1, "target": 5}, {"source": 2, "target": 5}, {"source": 3, "target": 5}]} | {"states": [0, 4], "expectation_value": -2.5198413533660764, "params": [0.0028, 0.5541, 0.0022, 0.4267, 0.8042, -0.0004, 0.0028, -0.5593, 0.0028, 0.5327000000000001, 0.0028, 0.0013000000000000002, 0.0022, 0.0036000000000000003, 0.8063, 0.0044, 0.0028, 0.001, 0.0028, 0.0016, -0.5137, -0.5407000000000001, -0.400400000000... | 0.25 * (Z(0) @ Z(1)) + 0.25 * (Z(0) @ Z(2)) + 0.25 * (Z(1) @ Z(2)) + -0.25 * (Z(0) @ Z(1) @ Z(2)) + 0.25 * (Z(3) @ Z(2)) + 0.25 * (Z(4) @ Z(2)) + 0.25 * (Z(3) @ Z(4)) + -0.25 * (Z(3) @ Z(4) @ Z(2)) + -0.75 * Z(0) + -0.75 * Z(1) + 0.0 * Z(2) + -0.75 * Z(3) + -0.75 * Z(4) | 18 | 5 | 2 | {"smallest_eigenvalues": [-3.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.0, "smallest_bitstrings": ["11011"], "largest_eigenvalue": 5.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[5] q;
rx(-0.06213685427517941) q[0];
rz(0.3900229257122323) q[0];
rx(-0.05273946885872852) q[1];
rz(0.8212831248228313) q[1];
rx(1.5337574379224534) q[2];
rz(0.18090279389762448) q[2];
rx(-0.062136854275179405) q[3];
rz(-0.7491475642969406) q[3];
rx(-0.062136854275179405) q[4... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIZZ",
"IIZIZ",
"IIZZI",
"IIZZZ",
"IZZII",
"ZIZII",
"ZZIII",
"ZZZII",
"IIIIZ",
"IIIZI",
"IIZII",
"IZIII",
"ZIIII"
] | [
0.25,
0.25,
0.25,
-0.25,
0.25,
0.25,
0.25,
-0.25,
-0.75,
-0.75,
0,
-0.75,
-0.75
] | 0.980175 | [
-0.062136854275179405,
0.5639668344247326,
-0.05273946885872852,
0.8212831248228313,
1.5337574379224534,
0.18090279389762448,
-0.7491475642969406,
0.5294660297481446,
-0.3478878174250011,
0.3529348580960014,
-0.022087508376134993,
-0.4435758830602262,
-0.5770407396054762,
-0.16077012495042... | {
"n_parameters": 24,
"n_qubits": 5,
"optimal_eigenvalue": -3,
"target_ratio": 0.97,
"target_value": -2.91
} | 6 |
d32bae70887cbda0fd64e6ae105154d4 | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"weight": 7, "source": 0, "target": 1}, {"weight": 13, "source": 0, "target": 6}, {"weight": 18, "source": 1, "target": 3}, {"weight": 8, "source": 2, "targ... | {"states": [252, 220], "expectation_value": -82.78256825901275, "params": [0.3821, 0.8496, 1.5897000000000001, 0.0064, 1.5810000000000002, 0.1449, 0.7814, 0.35710000000000003, 1.5786, 0.0037, 1.5856000000000001, -0.0011, 1.5838, 0.27740000000000004, 0.1429, 0.6975, 0.5484, -0.5028, 0.3902, 0.0027, 1.5785, 0.0086, 1.581... | 4.5 * (Z(0) @ Z(1)) + 4.5 * (Z(2) @ Z(0)) + 4.5 * (Z(3) @ Z(2)) + 4.5 * (Z(4) @ Z(2)) + 4.5 * (Z(4) @ Z(3)) + 4.5 * (Z(6) @ Z(2)) + 4.5 * (Z(6) @ Z(3)) + 4.5 * (Z(6) @ Z(4)) + 4.5 * (Z(5) @ Z(2)) + 4.5 * (Z(5) @ Z(3)) + 4.5 * (Z(5) @ Z(4)) + 4.5 * (Z(5) @ Z(6)) + 4.5 * (Z(7) @ Z(4)) + 4.5 * (Z(7) @ Z(5)) + 4.5 * (Z(8) ... | 18 | 9 | 2 | {"smallest_eigenvalues": [-91.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -82.0, "smallest_bitstrings": ["100100011"], "largest_eigenvalue": 189.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(0.1621346981994899) q[0];
rz(1.219855244128853) q[0];
rx(1.49996168361611) q[1];
rz(0.012973842691636614) q[1];
rx(1.8224941963463162) q[2];
rz(0.11473252339454168) q[2];
rx(0.35557846104245544) q[3];
rz(0.4777493280871876) q[3];
rx(1.7783067709589961) q[4];
rz(0.100... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum", "extra": "{\"n\": 8}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIZZ",
"IIIIIIZIZ",
"IIIIIZZII",
"IIIIZIZII",
"IIIIZZIII",
"IIZIIIZII",
"IIZIIZIII",
"IIZIZIIII",
"IIIZIIZII",
"IIIZIZIII",
"IIIZZIIII",
"IIZZIIIII",
"IZIIZIIII",
"IZIZIIIII",
"ZIIIIIIZI",
"ZIZIIIIII",
"IIIIIIIZI",
"IIIIIIIIZ",
"IIIIIIZII",
"IIIIIZIII",
"IIIIZIIII",
"... | [
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
6.5,
3.5,
22.5,
13,
21,
23.5,
21.5,
1,
4.5
] | 0.975155 | [
0.1621346981994899,
0.8907909437276,
1.49996168361611,
0.012973842691636614,
1.8224941963463162,
0.11473252339454168,
0.35557846104245544,
0.4777493280871876,
1.7783067709589961,
0.10092441617979156,
1.4152144998462595,
-0.06409716579262772,
1.6293285773649606,
0.15823143802141262,
0.028... | {
"n_parameters": 53,
"n_qubits": 9,
"optimal_eigenvalue": -91,
"target_ratio": 0.97,
"target_value": -88.27
} | 13 |
3270355524554715564 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8], "hyperedges": [[0, 3], [8, 6], [4, 6, 7], [0, 8], [0, 6], [0, 1], [1, 2], [5, 6]]} | {"states": [181, 180], "expectation_value": -0.3539494951497588, "params": [0.6945, -0.0049, 0.687, 0.0037, 0.7107, 0.005200000000000001, 0.7057, 0.0058000000000000005, 0.7064, 0.0031000000000000003, 0.5501, 0.006500000000000001, 0.7093, -0.002, 0.7020000000000001, 0.009600000000000001, 0.7077, -0.0011, 0.6970000000000... | 0.5 * (Z(0) @ Z(3)) + 0.5 * (Z(8) @ Z(0)) + 0.5 * (Z(6) @ Z(0)) + 0.5 * (Z(6) @ Z(8)) + 0.16666666666666666 * (Z(4) @ Z(6)) + 0.16666666666666666 * (Z(7) @ Z(6)) + 0.16666666666666666 * (Z(7) @ Z(4)) + 0.5 * (Z(1) @ Z(0)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(5) @ Z(6)) + 0.0 * Z(3) + 0.0 * Z(0) + 0.0 * Z(8) + 0.16666666666... | 6 | 9 | 1 | {"smallest_eigenvalues": [-2.833333333333334, -2.833333333333334, -2.833333333333334, -2.833333333333334, -2.833333333333334, -2.833333333333334], "number_of_smallest_eigenvalues": 6, "first_excited_energy": -2.833333333333333, "smallest_bitstrings": ["101011001", "010101011", "101011000", "010111001", "101001011", "10... | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(-0.08194362207734435) q[0];
rz(0.728519803177365) q[0];
rx(2.705179642232708) q[1];
rz(1.7709857213677775) q[1];
rx(0.2729617761235626) q[2];
rz(1.928884796645093) q[2];
rx(2.723966253077711) q[3];
rz(1.6835512139302065) q[3];
rx(0.7351924727397264) q[4];
rz(1.480803... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIZIIZ",
"ZIIIIIIIZ",
"IIZIIIIIZ",
"ZIZIIIIII",
"IIZIZIIII",
"IZZIIIIII",
"IZIIZIIII",
"IIIIIIIZZ",
"IIIIIIZZI",
"IIZZIIIII",
"IIIIIZIII",
"IIIIIIIIZ",
"ZIIIIIIII",
"IIZIIIIII",
"IIIIZIIII",
"IZIIIIIII",
"IIIIIIIZI",
"IIIIIIZII",
"IIIZIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.5,
0.5,
0,
0,
0,
0.16666666666666696,
0.16666666666666666,
0.16666666666666666,
0,
0,
0
] | 0.971492 | [
-0.08194362207734436,
-0.8422765236175316,
2.705179642232708,
0.20018939457288137,
0.27296177612356265,
0.35808846985019704,
2.723966253077711,
0.11275488713530996,
0.7351924727397263,
-0.08999301135594505,
-0.03289001825051979,
0.30352766837885364,
1.0469727952696977,
0.14091141406477398,... | {
"n_parameters": 45,
"n_qubits": 9,
"optimal_eigenvalue": -2.833333333333334,
"target_ratio": 0.97,
"target_value": -2.748333333333334
} | 122 |
59b55089c15cad6a91f754f2be38a436 | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 6}, {"source": 1, "target": 3}, {"source": 1, "target": 5}, {"source": 1, "target": 6}, {"source": 2, "target": 4}, ... | {"states": [247, 243], "expectation_value": -0.6590016101825699, "params": [1.4280000000000002, 0.009600000000000001, 1.1841000000000002, 0.0063, 1.7028, 0.0049, 1.7006000000000001, 0.006900000000000001, 1.7072, 0.0055000000000000005, 1.7015, 0.0039000000000000003, 0.45170000000000005, 0.0066, 1.4837, 0.003100000000000... | 0.5 * (Z(0) @ Z(1)) + 0.125 * (Z(0) @ Z(2)) + 0.125 * (Z(0) @ Z(3)) + 0.125 * (Z(0) @ Z(4)) + 0.125 * (Z(2) @ Z(3)) + 0.125 * (Z(4) @ Z(2)) + 0.125 * (Z(4) @ Z(3)) + -0.125 * (Z(0) @ Z(2) @ Z(3)) + -0.125 * (Z(0) @ Z(4) @ Z(2)) + -0.125 * (Z(0) @ Z(4) @ Z(3)) + -0.125 * (Z(4) @ Z(2) @ Z(3)) + 0.125 * (Z(0) @ Z(4) @ Z(2... | 16 | 10 | 1 | {"smallest_eigenvalues": [-3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25, -3.25], "number_of_smallest_eigenvalues": 16, "first_excited_energy": -2.25, "smallest_bitstrings": ["0101001100", "0100101100", "0101010010", "0110001100", "0110001001", "0111010000", "011... | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
rx(-2.930992925974156) q[0];
rz(-2.0505334193883) q[0];
rx(0.09974558989948948) q[1];
rz(-0.021916551230833636) q[1];
cx q[1], q[0];
rz(0.7487040703349622) q[0];
cx q[1], q[0];
rz(0.03143390177930412) q[1];
rx(3.064188251569036) q[2];
rz(1.260785857636634) q[2];
rx(3.1... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIIZZ",
"IIIIIIIZIZ",
"IIIIIIZIIZ",
"IIIIIZIIIZ",
"IIIIIIZZII",
"IIIIIZIZII",
"IIIIIZZIII",
"IIIIIIZZIZ",
"IIIIIZIZIZ",
"IIIIIZZIIZ",
"IIIIIZZZII",
"IIIIIZZZIZ",
"IIIZZIIIII",
"IIZIIIIZII",
"IZIIIIIZII",
"IZZIIIIIII",
"IZZIIIIZII",
"IIZIZIIIII",
"ZIIIZIIIII",
"ZIZIIIIIII"... | [
0.5,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.5,
0.25,
0.25,
0.25,
-0.25,
0.25,
0.25,
0.25,
-0.25,
0.5,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
-0.125,
-0.125,
0.1... | 0.978586 | [
3.352192381205431,
-1.3018293490533377,
0.09974558989948948,
-0.021916551230833636,
3.064188251569036,
1.0242823876125022,
3.1401663157651902,
-0.039487779968993025,
-0.24892087794353424,
0.13415136123448565,
3.4156926946764425,
0.5404877583717977,
0.05848107904958504,
0.21099505519505057,... | {
"n_parameters": 28,
"n_qubits": 10,
"optimal_eigenvalue": -3.25,
"target_ratio": 0.97,
"target_value": -3.1525
} | 50 |
aade6b836b57350e8a9bbf86526779e2 | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 0, "id": 3}, {"bipartite": 0, "id": 4}, {"bipartite": 0, "id": 5}, {"bipartite": 0, "id": 6}, {"bipartite": 0, "id": 7}, {"bipartite": 1, "id": 8}, {"bipartite":... | {"states": [399, 143], "expectation_value": -105.24636086589527, "params": [1.5363, 0.00030000000000000003, 3.0969, 0.0068000000000000005, 0.3765, 0.0, 0.0024000000000000002, 0.009600000000000001, 0.498, 0.0099, 3.0896000000000003, 0.0085, 3.0987, 0.007200000000000001, 3.0899, 0.0031000000000000003, 3.0886, 0.0027, 0.0... | 6.5 * (Z(0) @ Z(1)) + 6.5 * (Z(2) @ Z(1)) + 6.5 * (Z(5) @ Z(1)) + 6.5 * (Z(5) @ Z(0)) + 6.5 * (Z(6) @ Z(2)) + 6.5 * (Z(6) @ Z(5)) + 6.5 * (Z(4) @ Z(5)) + 6.5 * (Z(4) @ Z(6)) + 6.5 * (Z(7) @ Z(1)) + 6.5 * (Z(7) @ Z(0)) + 6.5 * (Z(7) @ Z(5)) + 6.5 * (Z(8) @ Z(1)) + 6.5 * (Z(8) @ Z(0)) + 6.5 * (Z(8) @ Z(5)) + 6.5 * (Z(8) ... | 18 | 9 | 1 | {"smallest_eigenvalues": [-115.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -104.5, "smallest_bitstrings": ["101110000"], "largest_eigenvalue": 251.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(0.8085890563793883) q[0];
rz(0.14909745412444142) q[0];
rx(3.073558291239385) q[1];
rz(0.19004506974858693) q[1];
rx(0.06140415702136045) q[2];
rz(-0.19845885848079203) q[2];
rx(-0.04484486135507425) q[3];
rz(0.10933068580131859) q[3];
rx(0.151893916801693) q[4];
rz(... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum_bipartite", "extra": "{\"left_nodes\": [0, 1, 2, 3, 4, 5, 6, 7], \"right_nodes\": [8, 9, 10, 11]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIZZ",
"IIIIIIZZI",
"IIIZIIIZI",
"IIIZIIIIZ",
"IIZIIIZII",
"IIZZIIIII",
"IIIZZIIII",
"IIZIZIIII",
"IZIIIIIZI",
"IZIIIIIIZ",
"IZIZIIIII",
"ZIIIIIIZI",
"ZIIIIIIIZ",
"ZIIZIIIII",
"ZZIIIIIII",
"IIIIIIIZI",
"IIIIIIIIZ",
"IIIIIIZII",
"IIIZIIIII",
"IIZIIIIII",
"IIIIZIIII",
"... | [
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
25.5,
17.5,
2,
36,
14.5,
3,
23,
23,
-9.5
] | 0.973656 | [
0.8085890563793883,
0.08320250699556596,
3.073558291239385,
0.19004506974858693,
0.06140415702136045,
-0.19845885848079203,
-0.04484486135507425,
0.10933068580131859,
0.151893916801693,
0.2402050987537897,
3.2417518992647527,
0.06004241881298271,
3.2487462856026186,
0.09269344766098876,
... | {
"n_parameters": 27,
"n_qubits": 9,
"optimal_eigenvalue": -115.5,
"target_ratio": 0.97,
"target_value": -112.035
} | 6 |
42fc1cab65130010b16c5206f9faaa99 | kclique | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 1, "target": 2}, {"source": 1, "ta... | {"states": [67, 7], "expectation_value": -6.26466472503126, "params": [[-0.013600000000000001, -0.0128, -0.0509], [0.0158, 0.017400000000000002, 0.0591]], "bitstrings": ["10111100", "11111000"], "total_optimization_steps": 10, "probabilities": [0.006719340641374812, 0.007071866989302057], "optimization_time": 8.4583806... | 2.75 * (Z(0) @ Z(1)) + 2.75 * (Z(2) @ Z(1)) + 2.75 * (Z(2) @ Z(0)) + 2.75 * (Z(3) @ Z(1)) + 2.75 * (Z(3) @ Z(0)) + 2.75 * (Z(3) @ Z(2)) + 2.75 * (Z(4) @ Z(1)) + 2.75 * (Z(4) @ Z(0)) + 2.75 * (Z(4) @ Z(2)) + 2.75 * (Z(4) @ Z(3)) + 3.0 * (Z(5) @ Z(1)) + 3.0 * (Z(5) @ Z(0)) + 2.75 * (Z(5) @ Z(2)) + 3.0 * (Z(5) @ Z(3)) + 3... | 4 | 8 | 3 | {"smallest_eigenvalues": [-24.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -21.5, "smallest_bitstrings": ["11111000"], "largest_eigenvalue": 135.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.020585712478965273) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(0.020585712478965273) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(0.020585712478965273) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(0.020585712478965273) q[3];
cx q[1], ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"k": 5} | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZZI",
"IIIIIZIZ",
"IIIIZIZI",
"IIIIZIIZ",
"IIIIZZII",
"IIIZIIZI",
"IIIZIIIZ",
"IIIZIZII",
"IIIZZIII",
"IIZIIIZI",
"IIZIIIIZ",
"IIZIIZII",
"IIZIZIII",
"IIZZIIII",
"IZIIIIZI",
"IZIIIIIZ",
"IZIIIZII",
"IZIIZIII",
"IZIZIIII",
"IZZIIIII",
"ZIIIIIZI",
"ZIIIIII... | [
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
2.75,
3,
3,
2.75,
3,
3,
2.75,
3,
3,
3,
3,
3,
3,
3,
2.75,
3,
3,
3,
2.75,
-7.25,
-7,
-7.5,
-7,
-7,
-6.25,
-6.5,
-6.5
] | 0.972491 | [
0.020585712478965273,
-0.10740732213659304,
0.9806179744216011,
1.2066222500302057,
0.807373465491872,
-0.7383480177614887,
-0.583309434460934,
1.229770317245662,
0.029731332749984192,
-0.4028832613860345,
-0.11890009039048421,
0.19530480659012922,
0.3300174811368061,
-0.05473954150926055,... | {
"n_parameters": 24,
"n_qubits": 8,
"optimal_eigenvalue": -24.5,
"target_ratio": 0.97,
"target_value": -23.765
} | 85 |
b2a86e79e509d0d76748a475959a4d60 | vertex_cover | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 3}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 1, "target": 5}, {"source": 2, "target": 6}, {"source": 3, "target": 5}, ... | {"states": [28, 86], "expectation_value": -1.3614314606011924, "params": [[0.0734, 0.07, 0.07300000000000001, 0.07740000000000001], [-0.0816, -0.0724, -0.0716, -0.0734]], "bitstrings": ["1100011", "0101001"], "total_optimization_steps": 10, "probabilities": [0.019466170144303175, 0.021360944494747937], "optimization_ti... | 0.5 * (Z(0) @ Z(3)) + 0.5 * (Z(1) @ Z(3)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(5) @ Z(3)) + 0.5 * (Z(5) @ Z(1)) + 0.5 * (Z(6) @ Z(3)) + 0.5 * (Z(6) @ Z(2)) + 0.5 * (Z(4) @ Z(6)) + -1.5 * Z(3) + 0.0 * Z(0) + -1.0 * Z(1) + -0.5 * Z(2) + -0.5 * Z(5) + -1.0 * Z(6) + 0.0 * Z(4) | 1 | 7 | 4 | {"smallest_eigenvalues": [-4.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -3.5, "smallest_bitstrings": ["0101001"], "largest_eigenvalue": 8.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
cx q[3], q[0];
rz(0.10531842151091338) q[0];
cx q[3], q[0];
rz(0.4891930059834122) q[0];
rx(-0.0661317683158416) q[0];
cx q[3], q[1];
rz(0.10531842151091338) q[1];
cx q[3], q[1];
cx q[1], q[2];
rz(0.10531842151091338) q[2];
cx q[1], q[2];... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIZIIZ",
"IIIZIZI",
"IIIIZZI",
"IZIZIII",
"IZIIIZI",
"ZIIZIII",
"ZIIIZII",
"ZIZIIII",
"IIIZIII",
"IIIIIIZ",
"IIIIIZI",
"IIIIZII",
"IZIIIII",
"ZIIIIII",
"IIZIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1.5,
0,
-1,
-0.5,
-0.5,
-1,
0
] | 0.981939 | [
0.10531842151091338,
-0.9612079782757411,
0.4891930059834108,
-0.3889941233568148,
0.09888614070956181,
-0.06613176831584158,
-0.15982742550497311,
-0.9131467726130178,
-0.7744447103826919,
0.963045529704064,
-0.42018965464630975,
0.1277451781058455,
0.12286825244091745,
-0.142262780034014... | {
"n_parameters": 20,
"n_qubits": 7,
"optimal_eigenvalue": -4.5,
"target_ratio": 0.97,
"target_value": -4.365
} | 44 |
-3476425399582412514 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7], "hyperedges": [[0, 7], [1, 3, 5], [0, 2, 5], [2, 3], [0, 1, 4], [4, 5, 6], [4, 6, 7], [0, 3], [1, 3, 6], [1, 2, 7], [4, 5, 7], [3, 6, 7], [1, 5, 7]]} | {"states": [234, 230], "expectation_value": -0.1015042767152605, "params": [[0.0609], [-0.055900000000000005]], "bitstrings": ["00010101", "00011001"], "total_optimization_steps": 10, "probabilities": [0.004213210696113554, 0.004231397621170056], "optimization_time": 2.981830358505249} | 0.5 * (Z(0) @ Z(7)) + 0.3333333333333333 * (Z(1) @ Z(7)) + 0.16666666666666666 * (Z(1) @ Z(0)) + 0.16666666666666666 * (Z(3) @ Z(7)) + 0.5 * (Z(3) @ Z(0)) + 0.3333333333333333 * (Z(3) @ Z(1)) + 0.3333333333333333 * (Z(5) @ Z(7)) + 0.16666666666666666 * (Z(5) @ Z(0)) + 0.3333333333333333 * (Z(5) @ Z(1)) + 0.166666666666... | 1 | 8 | 1 | {"smallest_eigenvalues": [-3.5000000000000004], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -3.4999999999999996, "smallest_bitstrings": ["00011001"], "largest_eigenvalue": 11.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
cx q[7], q[0];
rz(0.7440925655631874) q[0];
cx q[7], q[0];
cx q[7], q[1];
rz(0.25126835006295745) q[1];
cx q[7], q[1];
cx q[0], q[1];
rz(-0.0378944176780027) q[1];
cx q[0], q[1];
cx q[7], q[3];
rz(-0.037894... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
bit[8] c;
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
cx q[7], q[0];
rz(x0) q[0];
cx q[7], q[0];
cx q[7], q[1];
rz(x1) q[1];
cx q[... | null | {"circuits": [], "gradients": []} | [
"ZIIIIIIZ",
"ZIIIIIZI",
"IIIIIIZZ",
"ZIIIZIII",
"IIIIZIIZ",
"IIIIZIZI",
"ZIZIIIII",
"IIZIIIIZ",
"IIZIIIZI",
"IIZIZIII",
"ZIIIIZII",
"IIIIIZIZ",
"IIIIIZZI",
"IIIIZZII",
"IIZIIZII",
"ZIIZIIII",
"IIIZIIIZ",
"IIIZIIZI",
"IIZZIIII",
"ZZIIIIII",
"IZIIIIZI",
"IZIIZIII",
"IZZIIII... | [
0.5,
0.3333333333333333,
0.16666666666666666,
0.16666666666666666,
0.5,
0.3333333333333333,
0.3333333333333333,
0.16666666666666666,
0.3333333333333333,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.16666666666666666,
0.3333333333333333,
0... | 0.58749 | [
0.7440925655631874,
0.25126835006295745,
-0.0378944176780027,
0.7402995094836877,
0.8344421489600198,
-0.8081323979222689
] | {
"n_parameters": 6,
"n_qubits": 8,
"optimal_eigenvalue": -3.5000000000000004,
"target_ratio": 0.97,
"target_value": -3.3950000000000005
} | 162 |
159674029209513093 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5], "hyperedges": [[0, 2, 3, 4, 5], [1, 2, 3, 5], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 3], [0, 1, 3, 4, 5]]} | {"states": [45, 53], "expectation_value": -0.98909663971875, "params": [[-0.5675], [0.3735]], "bitstrings": ["010010", "001010"], "total_optimization_steps": 60, "probabilities": [0.03939136419676468, 0.03939136419676469], "optimization_time": 3.8801965713500977} | 0.3 * (Z(0) @ Z(2)) + 0.21666666666666667 * (Z(3) @ Z(2)) + 0.18333333333333335 * (Z(3) @ Z(0)) + 0.13333333333333333 * (Z(4) @ Z(2)) + 0.18333333333333335 * (Z(4) @ Z(0)) + 0.1 * (Z(4) @ Z(3)) + 0.21666666666666667 * (Z(5) @ Z(2)) + 0.18333333333333335 * (Z(5) @ Z(0)) + 0.18333333333333335 * (Z(5) @ Z(3)) + 0.1 * (Z(5... | 1 | 6 | 1 | {"smallest_eigenvalues": [-1.3166666666666669, -1.3166666666666669], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -1.3166666666666664, "smallest_bitstrings": ["001010", "010010"], "largest_eigenvalue": 6.000000000000001} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
h q[0];
h q[1];
h q[2];
cx q[2], q[0];
rz(3.7083113148980365e-08) q[0];
cx q[2], q[0];
h q[3];
cx q[2], q[3];
rz(1.962880927346927e-08) q[3];
cx q[2], q[3];
cx q[0], q[3];
rz(-2.646817199850091e-08) q[3];
cx q[0], q[3];
h q[4];
cx q[2], q[4];
rz(-8.835816843536436e-08) ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
input float[64] x9;
bit[6] c;
qubit[6] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];... | null | {"circuits": [], "gradients": []} | [
"IIIZIZ",
"IIZZII",
"IIZIIZ",
"IZIZII",
"IZIIIZ",
"IZZIII",
"ZIIZII",
"ZIIIIZ",
"ZIZIII",
"ZZIIII",
"IIIZZI",
"IIIIZZ",
"IIZIZI",
"IZIIZI",
"ZIIIZI",
"IIIZII",
"IIIIIZ",
"IIZIII",
"IZIIII",
"ZIIIII",
"IIIIZI"
] | [
0.3,
0.21666666666666667,
0.18333333333333335,
0.13333333333333333,
0.18333333333333335,
0.1,
0.21666666666666667,
0.18333333333333335,
0.18333333333333335,
0.1,
0.3333333333333333,
0.3,
0.21666666666666667,
0.13333333333333333,
0.21666666666666667,
0.6,
0.5750000000000002,
0.45000... | 0.902186 | [
3.7083113148980365e-8,
1.962880927346927e-8,
-2.646817199850091e-8,
-8.835816843536436e-8,
-1.33718120101323e-8,
5.86305267371123e-8,
-1.570796340797539,
1.570796408630983,
-0.576931242266165,
-1.5707964905985634,
1.5707962292841438
] | {
"n_parameters": 11,
"n_qubits": 6,
"optimal_eigenvalue": -1.3166666666666669,
"target_ratio": 0.97,
"target_value": -1.2771666666666668
} | 336 |
feaf30b79c91a036f216c182772bdb1d | connected_components | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}], "edges": [{"source": 0, "target": 1}, {"source": 2, "target": 3}, {"source": 2, "target": 4}, {"source": 2, "target": 5}, {"source": 4, "target": 5}, {"sour... | {"states": [60, 252], "expectation_value": -10.573244495668249, "params": null, "bitstrings": ["11000011", "00000011"], "total_optimization_steps": 81, "probabilities": [0.11554366625812093, 0.546588560715556], "optimization_time": 115.0621497631073} | -1.0 * (Z(0) @ Z(1)) + -2.0 * (Z(2) @ Z(3)) + 0.5 * (Z(4) @ Z(3)) + -2.0 * (Z(4) @ Z(2)) + 0.5 * (Z(5) @ Z(3)) + -2.0 * (Z(5) @ Z(2)) + -1.5 * (Z(5) @ Z(4)) + -1.5 * (Z(6) @ Z(7)) + 0.5 * Z(1) + 0.5 * Z(0) + 0.5 * Z(3) + 0.5 * Z(2) + 0.5 * Z(4) + 0.5 * Z(5) + -1.0 * Z(7) + -1.0 * Z(6) | 1 | 8 | 1 | {"smallest_eigenvalues": [-14.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -12.0, "smallest_bitstrings": ["00000011"], "largest_eigenvalue": 9.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
ry(0.6880001825840584) q[0];
h q[1];
cx q[1], q[0];
ry(-0.6880001825840584) q[0];
cx q[1], q[0];
ry(0.5494202574096909) q[1];
cx q[0], q[1];
ry(-0.5494202574096909) q[1];
cx q[0], q[1];
h q[2];
ry(0.011133946782301766) q[2];
h q[3];
ry(1.9661753510022562) q[3];
... | null | {"node": 7} | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[8] c;\nqubit[8] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\ncry(1.5706) q[5], q[2];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = mea... | [
"IIIIIIZZ",
"IIIIZZII",
"IIIZZIII",
"IIIZIZII",
"IIZIZIII",
"IIZIIZII",
"IIZZIIII",
"ZZIIIIII",
"IIIIIIZI",
"IIIIIIIZ",
"IIIIZIII",
"IIIIIZII",
"IIIZIIII",
"IIZIIIII",
"ZIIIIIII",
"IZIIIIII"
] | [
-1,
-2,
0.5,
-2,
0.5,
-2,
-1.5,
-1.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1,
-1
] | 0.964834 | [
0.02226789356460353,
2.8818319024337766,
-0.8942463794901929,
3.178663541717695,
3.9323507020045123,
-1.257886419085656,
-1.5772014760986535,
1.3760003651681167,
1.0988405148193818,
-1.1868547387115274,
-0.9947629393548405,
-0.056348868541210614,
-0.02223055365976749,
-0.33130717160864015,... | {
"n_parameters": 35,
"n_qubits": 8,
"optimal_eigenvalue": -14,
"target_ratio": 0.97,
"target_value": -13.58
} | 500 |
4cd28f9bc761b26f6d6f15aeccbaedea | matching | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"weight": 9, "source": 0, "target": 1}, {"weight": 11, "source": 0, "target": 4}, {"weight": 18, "source": 0, "target": 5}, {"weight": 20, "source": 0, "target": 3}, {... | {"states": [122, 121], "expectation_value": -29.787190062500652, "params": [[-0.029300000000000003, -0.0158, 0.0035, 0.0165], [0.0526, 0.0616, 0.0674, 0.061000000000000006]], "bitstrings": ["10000101", "10000110"], "total_optimization_steps": 10, "probabilities": [0.01672834613389989, 0.01820252621087309], "optimizatio... | 4.0 * (Z(0) @ Z(1)) + 4.0 * (Z(2) @ Z(1)) + 4.0 * (Z(2) @ Z(0)) + 4.0 * (Z(3) @ Z(1)) + 4.0 * (Z(3) @ Z(0)) + 4.0 * (Z(3) @ Z(2)) + 4.0 * (Z(4) @ Z(0)) + 4.0 * (Z(5) @ Z(1)) + 4.0 * (Z(6) @ Z(2)) + 4.0 * (Z(6) @ Z(3)) + 4.0 * (Z(7) @ Z(2)) + 4.0 * (Z(7) @ Z(4)) + 4.0 * (Z(7) @ Z(6)) + 18.0 * Z(1) + 12.5 * Z(0) + 17.5 *... | 1 | 8 | 4 | {"smallest_eigenvalues": [-63.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -58.0, "smallest_bitstrings": ["10000110"], "largest_eigenvalue": 145.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.00016732716707271525) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(0.00016732716707271525) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(0.00016732716707271525) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(0.00016732716707271525) q[3];
c... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum", "extra": "{\"n\": 7}"} | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZZI",
"IIIIIZIZ",
"IIIIZIZI",
"IIIIZIIZ",
"IIIIZZII",
"IIIZIIIZ",
"IIZIIIZI",
"IZIIIZII",
"IZIIZIII",
"ZIIIIZII",
"ZIIZIIII",
"ZZIIIIII",
"IIIIIIZI",
"IIIIIIIZ",
"IIIIIZII",
"IIIIZIII",
"IIIZIIII",
"IIZIIIII",
"IZIIIIII",
"ZIIIIIII"
] | [
4,
4,
4,
4,
4,
4,
4,
4,
4,
4,
4,
4,
4,
18,
12.5,
17.5,
17,
8.5,
0,
8.5,
11
] | 0.920635 | [
0.00016732716707271525,
-0.5924455788903747,
1.1202157596152196,
-2.1299919140966863,
-0.921283751470345,
-0.9259638537657344,
0.656788748097326,
0.05566707846777746,
-0.2350099582362983,
-0.00025338828965832576,
-0.7056870444167618,
0.6002165622279372,
0.40321396654204583,
-0.860670749125... | {
"n_parameters": 33,
"n_qubits": 8,
"optimal_eigenvalue": -63,
"target_ratio": 0.97,
"target_value": -61.11
} | 500 |
dcc91cdbd34687cb4cde0159b3b69295 | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"capacity": 6, "source": 0, "target": 2}, {"capacity": 4, "source": 0, "target": 4}, {"capacity": 2, "source": 0, "target": 5}, {"capacity": 4, "source": 1, "target": 3}, {"capaci... | {"states": [62, 1], "expectation_value": -1.531547568443565, "params": [[-0.0455, 0.0458, 0.06860000000000001], [0.0713, 0.0086, -0.044000000000000004]], "bitstrings": ["000001", "111110"], "total_optimization_steps": 10, "probabilities": [0.023110989201895336, 0.027831702809345805], "optimization_time": 3.811333656311... | -1.5 * (Z(0) @ Z(2)) + -1.0 * (Z(4) @ Z(0)) + -0.5 * (Z(5) @ Z(2)) + 2.75 * (Z(5) @ Z(0)) + -1.5 * (Z(1) @ Z(2)) + -1.25 * (Z(1) @ Z(4)) + -1.5 * (Z(3) @ Z(2)) + -1.5 * (Z(3) @ Z(4)) + -1.0 * (Z(3) @ Z(1)) + -1.0 * Z(2) + -0.25 * Z(0) + -3.75 * Z(4) + 2.25 * Z(5) + 0.75 * Z(1) + 2.0 * Z(3) | 1 | 6 | 3 | {"smallest_eigenvalues": [-16.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -12.0, "smallest_bitstrings": ["111110"], "largest_eigenvalue": 20.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
h q[0];
h q[1];
h q[2];
cx q[2], q[0];
rz(-0.044664277725590396) q[0];
cx q[2], q[0];
h q[3];
h q[4];
cx q[0], q[4];
rz(0.9476165902599167) q[4];
cx q[0], q[4];
h q[5];
cx q[2], q[5];
rz(0.2197380806591726) q[5];
cx q[2], q[5];
cx q[0], q[5];
cx q[2], q[1];
rz(-0.044664... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"source": 0, "sink": 5} | {"circuits": [], "gradients": []} | [
"IIIZIZ",
"IZIIIZ",
"ZIIZII",
"ZIIIIZ",
"IIIZZI",
"IZIIZI",
"IIZZII",
"IZZIII",
"IIZIZI",
"IIIZII",
"IIIIIZ",
"IZIIII",
"ZIIIII",
"IIIIZI",
"IIZIII"
] | [
-1.5,
-1,
-0.5,
2.75,
-1.5,
-1.25,
-1.5,
-1.5,
-1,
-1,
-0.25,
-3.75,
2.25,
0.75,
2
] | 0.971285 | [
-0.044664277725590396,
0.9476165902599167,
0.2197380806591726,
-1.0514987471546466,
0.7957038260820295,
0.9413668686439479,
0.30213414012420514,
-0.21178742517058777,
-0.276000794237401,
-0.56205179495253,
-0.048813665783677476,
0.00872254323661896,
-1.560904246060386,
-0.16892054994762315... | {
"n_parameters": 33,
"n_qubits": 6,
"optimal_eigenvalue": -16,
"target_ratio": 0.97,
"target_value": -15.52
} | 244 |
69813e7e1ac3357c75564eae7cbbd456 | connected_components | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}, {"id": 10}, {"id": 11}, {"id": 12}, {"id": 13}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 3}, {"source": 1, "target": 2}, {"s... | {"states": [8191, 8063], "expectation_value": -16.314668036931145, "params": [[[-1.1919, 2.3445], [-0.0031000000000000003, 0.7685000000000001], [0.0029000000000000002, -0.0032], [0.0018000000000000002, 0.0021000000000000003], [-0.0028, 0.0021000000000000003], [1.6664, -0.0018000000000000002], [0.0017000000000000001, 0.... | -1.5 * (Z(0) @ Z(6)) + 0.5 * (Z(5) @ Z(0)) + -1.5 * (Z(7) @ Z(8)) + -1.5 * (Z(9) @ Z(8)) + -1.5 * (Z(9) @ Z(7)) + -2.0 * (Z(10) @ Z(11)) + -2.0 * (Z(12) @ Z(11)) + 0.5 * (Z(12) @ Z(10)) + -2.0 * (Z(1) @ Z(11)) + 0.5 * (Z(1) @ Z(10)) + 0.5 * (Z(1) @ Z(12)) + -1.5 * (Z(2) @ Z(3)) + 0.5 * (Z(4) @ Z(3)) + -1.5 * (Z(4) @ Z(... | 15 | 13 | 1 | {"smallest_eigenvalues": [-19.0, -19.0], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -18.0, "smallest_bitstrings": ["1000011000000", "0000010000000"], "largest_eigenvalue": 20.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[13] q;
ry(-0.1912780613085044) q[0];
ry(0.06392243705412673) q[1];
ry(-0.17999027111555135) q[2];
ry(0.02192904651504507) q[3];
ry(-0.03592360773156095) q[4];
ry(2.8263018684412065) q[5];
ry(0.20809507620210096) q[6];
ry(-0.008401185124138705) q[7];
ry(-0.008401185124138705) ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64]... | {"node": 1} | {"circuits": [], "gradients": []} | [
"IIIIIIZIIIIIZ",
"IIIIIIIZIIIIZ",
"IIIIZZIIIIIII",
"IIIZZIIIIIIII",
"IIIZIZIIIIIII",
"IZZIIIIIIIIII",
"ZZIIIIIIIIIII",
"ZIZIIIIIIIIII",
"IZIIIIIIIIIZI",
"IIZIIIIIIIIZI",
"ZIIIIIIIIIIZI",
"IIIIIIIIIZZII",
"IIIIIIIIZZIII",
"IIIIIIIIZIZII",
"IIIIIIZIIIIII",
"IIIIIIIIIIIIZ",
"IIIIIIIZIII... | [
-1.5,
0.5,
-1.5,
-1.5,
-1.5,
-2,
-2,
0.5,
-2,
0.5,
0.5,
-1.5,
0.5,
-1.5,
1,
-1.5,
-1,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5
] | 0.9733 | [
-0.1912780613085044,
0.06392243705412673,
-0.17999027111555135,
0.02192904651504507,
-0.03592360773156095,
2.8263018684412065,
0.20809507620210096,
-0.008401185124138705,
0.2100223753448772,
-0.10312985557626862,
3.1818797226526163,
0.03887070098547564,
-0.0341488334394625,
-0.015076400294... | {
"n_parameters": 17,
"n_qubits": 13,
"optimal_eigenvalue": -19,
"target_ratio": 0.97,
"target_value": -18.43
} | 27 |
a9df2c16e7d96c32af9751f0e1a9f46a | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"source": 0, "target": 5}, {"source": 0, "target": 6}, {"source": 1, "target": 5}, {"source": 2, "target": 3}, {"source": 2, "target": 4}, {"source": 2, "ta... | {"states": [1139, 1147], "expectation_value": -1.171272681484499, "params": [0.7998000000000001, 0.8067000000000001, 0.2919, 0.2911, 0.0025, 0.0023, 0.6551, 0.6566000000000001, 0.8046000000000001, 0.8016000000000001, 0.8103, 0.8084, 0.798, 0.8023, 0.7973, 0.7973, 0.553, 0.5526, 0.8067000000000001, 0.8078000000000001, 0... | 0.5 * (Z(0) @ Z(1)) + 0.125 * (Z(3) @ Z(4)) + 0.125 * (Z(3) @ Z(5)) + 0.125 * (Z(3) @ Z(6)) + 0.125 * (Z(4) @ Z(5)) + 0.125 * (Z(4) @ Z(6)) + 0.125 * (Z(5) @ Z(6)) + -0.125 * (Z(3) @ Z(4) @ Z(5)) + -0.125 * (Z(3) @ Z(4) @ Z(6)) + -0.125 * (Z(3) @ Z(5) @ Z(6)) + -0.125 * (Z(4) @ Z(5) @ Z(6)) + 0.125 * (Z(3) @ Z(4) @ Z(5... | 13 | 11 | 1 | {"smallest_eigenvalues": [-4.90625], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -3.90625, "smallest_bitstrings": ["01110000100"], "largest_eigenvalue": 7.09375} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
ry(0.9062625778470087) q[0];
rz(0.1469040189925021) q[0];
ry(0.04688011247713439) q[1];
ry(-0.035280598705792324) q[2];
ry(0.2603406271841221) q[3];
ry(1.0030732452165743) q[4];
ry(1.7089166071150488) q[5];
ry(2.3667584163061086) q[6];
ry(1.6127464577692254) q[7];
ry(0... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIIIZZ",
"IIIIIIZZIII",
"IIIIIZIZIII",
"IIIIZIIZIII",
"IIIIIZZIIII",
"IIIIZIZIIII",
"IIIIZZIIIII",
"IIIIIZZZIII",
"IIIIZIZZIII",
"IIIIZZIZIII",
"IIIIZZZIIII",
"IIIIZZZZIII",
"IIIZIIIZIII",
"IIZIIIZIIII",
"IIIIIIIIZIZ",
"IIIIIZIIIIZ",
"IIIZIIIIIIZ",
"IZIIIIIIIIZ",
"ZIIIIIIII... | [
0.5,
0.125,
0.125,
0.125,
0.125,
0.125,
0.125,
-0.125,
-0.125,
-0.125,
-0.125,
0.125,
0.5,
0.5,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
-0.03125,
-0.03125,
-0.... | 0.98346 | [
0.9062625778470087,
0.04688011247713439,
-0.035280598705792324,
0.2603406271841221,
1.0030732452165743,
1.7089166071150488,
2.3667584163061086,
1.6127464577692254,
0.001588727257674491,
2.203277107831404,
1.7373195780478687,
0.2938080379850042,
0.1068690756630959,
0.7217816754589331,
-0.... | {
"n_parameters": 40,
"n_qubits": 11,
"optimal_eigenvalue": -4.90625,
"target_ratio": 0.97,
"target_value": -4.7590625
} | 58 |
2933316839893753680 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], "hyperedges": [[8, 6], [0, 2, 4], [1, 3, 9], [9, 4, 7], [5, 6], [1, 4, 5], [0, 1, 2, 3, 5, 7, 8], [9, 3, 4], [9, 2, 5, 7], [0, 10, 3], [0, 4, 5, 9, 10], [8, 1, 10, 4], [10, 2, 6, 7], [1, 2, 3, 5, 7, 8, 10], [2, 4, 5, 7]]} | {"states": [423, 487], "expectation_value": -3.7023587601803154, "params": [0.162, 0.16160000000000002, 0.1636, 0.1721, 1.5797, 1.5679, 1.5730000000000002, 1.5724, 0.8524, 0.8541000000000001, 1.5698, 1.5675000000000001, 0.0031000000000000003, 0.0029000000000000002, 0.257, 0.3538, 1.5727, 1.5752000000000002, 1.5696, 1.5... | 0.5 * (Z(8) @ Z(6)) + 0.023809523809523808 * (Z(0) @ Z(8)) + 0.08333333333333333 * (Z(2) @ Z(6)) + 0.047619047619047616 * (Z(2) @ Z(8)) + 0.19047619047619047 * (Z(2) @ Z(0)) + 0.08333333333333333 * (Z(4) @ Z(8)) + 0.21666666666666667 * (Z(4) @ Z(0)) + 0.25 * (Z(4) @ Z(2)) + 0.13095238095238093 * (Z(1) @ Z(8)) + 0.02380... | 13 | 11 | 1 | {"smallest_eigenvalues": [-4.116666666666667], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -4.000000000000001, "smallest_bitstrings": ["11000011000"], "largest_eigenvalue": 14.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
ry(0.09203576054881435) q[0];
rz(0.07138600098171655) q[0];
ry(0.40808190491906526) q[1];
ry(1.5241843067813186) q[2];
ry(1.5161322233634391) q[3];
ry(1.3333213829536812) q[4];
ry(1.5022013389948532) q[5];
ry(-0.1444429819401617) q[6];
ry(0.0783401415352531) q[7];
ry(1... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIZIZIIIIII",
"IIZIIIIIIIZ",
"IIIIZIIIZII",
"IIZIIIIIZII",
"IIIIIIIIZIZ",
"IIZIIIZIIII",
"IIIIIIZIIIZ",
"IIIIIIZIZII",
"IIZIIIIIIZI",
"IIIIIIIIIZZ",
"IIIIIIIIZZI",
"IIIIIIZIIZI",
"IIZIIIIZIII",
"IIIIIIIZIIZ",
"IIIIIIIZZII",
"IIIIIIZZIII",
"IIIIIIIZIZI",
"IZIIIIIIIIZ",
"IZIIIIIIZ... | [
0.5,
0.023809523809523808,
0.08333333333333333,
0.047619047619047616,
0.19047619047619047,
0.08333333333333333,
0.21666666666666667,
0.25,
0.13095238095238093,
0.023809523809523808,
0.047619047619047616,
0.25,
0.047619047619047616,
0.19047619047619047,
0.047619047619047616,
0.166666666... | 0.970813 | [
0.09203576054881435,
0.40808190491906526,
1.5241843067813186,
1.5161322233634391,
1.3333213829536812,
1.5022013389948532,
-0.1444429819401617,
0.0783401415352531,
1.7368307394885794,
1.840957086119496,
1.3646608143696093,
0.1427720019634331,
0.17454805879947116,
0.24834013862259677,
-0.2... | {
"n_parameters": 42,
"n_qubits": 11,
"optimal_eigenvalue": -4.116666666666667,
"target_ratio": 0.97,
"target_value": -3.993166666666667
} | 9 |
df4ecb6ebc48c9049ce6597f2a05ee78 | matching | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"weight": 1, "source": 0, "target": 1}, {"weight": 13, "source": 1, "target": 7}, {"weight": 20, "source": 1, "target": 6}, {"weight": 18, "source": 1, "tar... | {"states": [246, 244], "expectation_value": -9.255437475911567, "params": [[-0.035], [0.048600000000000004]], "bitstrings": ["100001001", "100001011"], "total_optimization_steps": 10, "probabilities": [0.0032254612952172103, 0.0034854804744819034], "optimization_time": 3.6021711826324463} | 4.5 * (Z(0) @ Z(2)) + 4.5 * (Z(4) @ Z(2)) + 4.5 * (Z(4) @ Z(0)) + 4.5 * (Z(3) @ Z(2)) + 4.5 * (Z(3) @ Z(0)) + 4.5 * (Z(3) @ Z(4)) + 4.5 * (Z(1) @ Z(2)) + 4.5 * (Z(1) @ Z(0)) + 4.5 * (Z(1) @ Z(4)) + 4.5 * (Z(1) @ Z(3)) + 4.5 * (Z(5) @ Z(1)) + 4.5 * (Z(6) @ Z(4)) + 4.5 * (Z(6) @ Z(5)) + 4.5 * (Z(7) @ Z(2)) + 4.5 * (Z(8) ... | 1 | 9 | 1 | {"smallest_eigenvalues": [-99.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -91.5, "smallest_bitstrings": ["100001011"], "largest_eigenvalue": 200.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
h q[1];
h q[2];
cx q[2], q[0];
rz(0.06360886017765513) q[0];
cx q[2], q[0];
h q[3];
h q[4];
cx q[2], q[4];
rz(0.06360886017765513) q[4];
cx q[2], q[4];
cx q[0], q[4];
cx q[2], q[3];
rz(0.06360886017765513) q[3];
cx q[2], q[3];
cx q[2], q[1];
rz(0.063608860177655... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
input float[64] x9;
bit[9] c;
qubit[9] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];... | {"matching": "perfect", "extra": "{\"n\": 8}"} | {"circuits": [], "gradients": []} | [
"IIIIIIZIZ",
"IIIIZIZII",
"IIIIZIIIZ",
"IIIIIZZII",
"IIIIIZIIZ",
"IIIIZZIII",
"IIIIIIZZI",
"IIIIIIIZZ",
"IIIIZIIZI",
"IIIIIZIZI",
"IIIZIIIZI",
"IIZIZIIII",
"IIZZIIIII",
"IZIIIIZII",
"ZIIIZIIII",
"ZIIIIZIII",
"ZIZIIIIII",
"IIIIIIZII",
"IIIIIIIIZ",
"IIIIZIIII",
"IIIIIZIII",
"... | [
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
22.5,
9.5,
24.5,
23.5,
22,
4,
12.5,
0.5,
5
] | 0.973782 | [
0.06360886017765513,
-1.5563439684684441,
1.389431623627156,
-1.70286799248886,
-1.6149385518993675,
-1.587244180675205,
1.2314295841410297,
-1.363684678698497,
1.3524507360679219,
1.6479140891865915,
1.6801288961870093
] | {
"n_parameters": 11,
"n_qubits": 9,
"optimal_eigenvalue": -99.5,
"target_ratio": 0.97,
"target_value": -96.515
} | 48 |
6444895837937385223 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5], "hyperedges": [[0, 2], [0, 1, 3], [2, 4], [2, 5]]} | {"states": [51, 28], "expectation_value": -0.590437106689168, "params": [[0.36710000000000004], [-0.3662]], "bitstrings": ["001100", "100011"], "total_optimization_steps": 40, "probabilities": [0.04043545537504582, 0.040603748606629624], "optimization_time": 1.4189982414245605} | 0.5 * (Z(0) @ Z(2)) + 0.16666666666666666 * (Z(1) @ Z(0)) + 0.16666666666666666 * (Z(3) @ Z(0)) + 0.16666666666666666 * (Z(3) @ Z(1)) + 0.5 * (Z(4) @ Z(2)) + 0.5 * (Z(5) @ Z(2)) + 0.0 * Z(2) + 0.16666666666666663 * Z(0) + 0.16666666666666666 * Z(1) + 0.16666666666666666 * Z(3) + 0.0 * Z(4) + 0.0 * Z(5) | 1 | 6 | 1 | {"smallest_eigenvalues": [-1.8333333333333335], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -1.833333333333333, "smallest_bitstrings": ["100011"], "largest_eigenvalue": 2.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
h q[0];
h q[1];
h q[2];
cx q[2], q[0];
rz(0.8990584604962922) q[0];
cx q[2], q[0];
cx q[0], q[1];
rz(0.3972565922143355) q[1];
cx q[0], q[1];
h q[3];
cx q[0], q[3];
rz(0.3972565922143355) q[3];
cx q[0], q[3];
rz(0.3972565922143354) q[0];
rx(-0.7875415688353298) q[0];
cx... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
bit[6] c;
qubit[6] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
cx q[2], q[0];
rz(x0) q[0];
cx q[2], q[0];
cx q[0], q[1];
rz(x1) q[1];
cx q[0], q[1];
cx q[0], q[3];
rz(x1) q[3];
cx q[0], q[3];
cx ... | null | {"circuits": [], "gradients": []} | [
"IIIZIZ",
"IIIIZZ",
"IIZIIZ",
"IIZIZI",
"IZIZII",
"ZIIZII",
"IIIZII",
"IIIIIZ",
"IIIIZI",
"IIZIII",
"IZIIII",
"ZIIIII"
] | [
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.5,
0,
0.16666666666666663,
0.16666666666666666,
0.16666666666666666,
0,
0
] | 0.529381 | [
0.8990584604962922,
0.3972565922143355,
-0.03174175485354618,
-0.7875415688353298
] | {
"n_parameters": 4,
"n_qubits": 6,
"optimal_eigenvalue": -1.8333333333333335,
"target_ratio": 0.97,
"target_value": -1.7783333333333333
} | 108 |
9a4ba729115cab9e89cb59ee0f761092 | community_detection | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"weight": 1, "source": 0, "target": 2}, {"weight": 1, "source": 0, "target": 3}, {"weight": 1, "source": 1, "target": 2}, {"weight": 1, "source": 1, "target... | {"states": [43605, 21930], "expectation_value": -0.02351808060435834, "params": [[-0.07780000000000001], [0.07680000000000001]], "bitstrings": ["0101010110101010", "1010101001010101"], "total_optimization_steps": 10, "probabilities": [1.677255175800303e-05, 1.677255175800304e-05], "optimization_time": 13.40773749351501... | 0.25 * (Z(0) @ Z(1)) + 0.00025000000000000006 * (Z(2) @ Z(0)) + 0.00025000000000000006 * (Z(3) @ Z(1)) + 0.25 * (Z(3) @ Z(2)) + -0.0008749999999999999 * (Z(4) @ Z(0)) + -0.0008749999999999999 * (Z(4) @ Z(2)) + -0.0008749999999999999 * (Z(5) @ Z(1)) + -0.0008749999999999999 * (Z(5) @ Z(3)) + 0.25 * (Z(5) @ Z(4)) + -0.00... | 5 | 16 | 1 | {"smallest_eigenvalues": [-2.023124999999981], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.023124999999973, "smallest_bitstrings": ["1010101001010101"], "largest_eigenvalue": NaN} | OPENQASM 3.0;
include "stdgates.inc";
qubit[16] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(-1.5943786181749542) q[0];
cx q[1], q[0];
h q[2];
cx q[0], q[2];
rz(-0.03376059023434233) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(-0.03376059023434233) q[3];
cx q[1], q[3];
cx q[2], q[3];
rz(-1.5943786181749542) q[3];
cx q[2], q... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
bit[16] c;
qubit[16] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
h q[8];
h q[9];
h q[10];
h q[11];
h q[12];
h q[13];
h q[14];
h q[15];
cx q... | {"communities_size": 4, "number_of_communities": 2} | {"circuits": [], "gradients": []} | [
"IIIIIIIIIIIIIIZZ",
"IIIIIIIIIIIIIZIZ",
"IIIIIIIIIIIIZIZI",
"IIIIIIIIIIIIZZII",
"IIIIIIIIIIIZIIIZ",
"IIIIIIIIIIIZIZII",
"IIIIIIIIIIZIIIZI",
"IIIIIIIIIIZIZIII",
"IIIIIIIIIIZZIIII",
"IIIIIIIIIZIIIIIZ",
"IIIIIIIIIZIIIZII",
"IIIIIIIIIZIZIIII",
"IIIIIIIIZIIIIIZI",
"IIIIIIIIZIIIZIII",
"IIIIIII... | [
0.25,
0.00025000000000000006,
0.00025000000000000006,
0.25,
-0.0008749999999999999,
-0.0008749999999999999,
-0.0008749999999999999,
-0.0008749999999999999,
0.25,
-0.00075,
-0.00075,
-0.0005000000000000001,
-0.00075,
-0.00075,
-0.0005000000000000001,
0.25,
0.000375,
0.000375,
0.00... | 0.98256 | [
-1.5943786181749542,
-0.03376059023434233,
0.0445299660384916,
0.015643914092638066,
-0.020345081953027686,
0.8076926259419518
] | {
"n_parameters": 6,
"n_qubits": 16,
"optimal_eigenvalue": -2.023124999999981,
"target_ratio": 0.97,
"target_value": -1.9624312499999816
} | 22 |
2c8d5f9e23ee6d88333a71ac770463ca | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 0, "id": 3}, {"bipartite": 0, "id": 4}, {"bipartite": 0, "id": 5}, {"bipartite": 1, "id": 6}, {"bipartite": 1, "id": 7}, {"bipartite": 1, "id": 8}, {"bipartite":... | {"states": [337, 849], "expectation_value": -117.39710597308836, "params": [[0.0024000000000000002, 0.1598, 0.7537, 0.1411, 0.8258000000000001, 0.0702, 0.8758, -0.0988, 0.0026000000000000003, -0.0723, 0.8048000000000001], [0.0024000000000000002, 0.7927000000000001, 0.9893000000000001, -0.20520000000000002, 0.8062, -0.0... | 8.0 * (Z(1) @ Z(3)) + 8.0 * (Z(2) @ Z(3)) + 8.0 * (Z(2) @ Z(1)) + 8.0 * (Z(6) @ Z(4)) + 8.0 * (Z(5) @ Z(4)) + 8.0 * (Z(5) @ Z(6)) + 8.0 * (Z(7) @ Z(6)) + 8.0 * (Z(10) @ Z(6)) + 8.0 * (Z(10) @ Z(7)) + 8.0 * (Z(9) @ Z(4)) + 8.0 * (Z(9) @ Z(10)) + 2.0 * Z(3) + 6.0 * Z(1) + 7.5 * Z(2) + 14.0 * Z(4) + 24.5 * Z(6) + 1.0 * Z(... | 10 | 11 | 3 | {"smallest_eigenvalues": [-123.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -115.0, "smallest_bitstrings": ["10010101110"], "largest_eigenvalue": 188.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
ry(0.1084508118083173) q[0];
ry(0.018743647892763803) q[1];
ry(0.7413327883813773) q[2];
ry(0.1302193755229099) q[3];
ry(0.7849881300480566) q[4];
ry(0.00491553005594016) q[5];
ry(0.7816314089261608) q[6];
ry(-0.11122429864034256) q[7];
ry(0.00822458118442003) q[8];
ry... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum_bipartite", "extra": "{\"left_nodes\": [0, 1, 2, 3, 4, 5], \"right_nodes\": [6, 7, 8, 9, 10, 11, 12, 13, 14]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIZIZI",
"IIIIIIIZZII",
"IIIIIIIIZZI",
"IIIIZIZIIII",
"IIIIIZZIIII",
"IIIIZZIIIII",
"IIIZZIIIIII",
"ZIIIZIIIIII",
"ZIIZIIIIIII",
"IZIIIIZIIII",
"ZZIIIIIIIII",
"IIIIIIIZIII",
"IIIIIIIIIZI",
"IIIIIIIIZII",
"IIIIIIZIIII",
"IIIIZIIIIII",
"IIIIIZIIIII",
"IIIZIIIIIII",
"ZIIIIIIII... | [
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
2,
6,
7.5,
14,
24.5,
1,
5,
14.5,
0.5,
-12.5,
-12.5
] | 0.973729 | [
0.1084508118083173,
0.018743647892763803,
0.7413327883813773,
0.1302193755229099,
0.7849881300480566,
0.00491553005594016,
0.7816314089261608,
-0.11122429864034256,
0.00822458118442003,
-0.048316222588891025,
0.7633463845650216,
1.0488375498271882,
0.9575966492377432,
-0.31290100010114463,... | {
"n_parameters": 40,
"n_qubits": 11,
"optimal_eigenvalue": -123,
"target_ratio": 0.97,
"target_value": -119.31
} | 11 |
f2268dbc2cd9e9d8be6517cd34bc9399 | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}], "edges": [{"capacity": 5, "source": 0, "target": 2}, {"capacity": 1, "source": 0, "target": 3}, {"capacity": 1, "source": 1, "target": 2}, {"capacity": 6, "source": 1, "target": 3}]} | {"states": [10, 5], "expectation_value": -0.22264524387252987, "params": [[-0.0502], [0.0644]], "bitstrings": ["0101", "1010"], "total_optimization_steps": 10, "probabilities": [0.06595400298934176, 0.07191507312239326], "optimization_time": 1.1569836139678955} | -1.25 * (Z(0) @ Z(2)) + 1.5 * (Z(3) @ Z(0)) + -0.25 * (Z(1) @ Z(2)) + -1.5 * (Z(1) @ Z(3)) + -1.5 * Z(2) + -0.25 * Z(0) + 0.0 * Z(3) + 1.75 * Z(1) | 1 | 4 | 1 | {"smallest_eigenvalues": [-7.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.5, "smallest_bitstrings": ["1010"], "largest_eigenvalue": 5.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[4] q;
h q[0];
h q[1];
h q[2];
cx q[2], q[0];
rz(0.08466080018590566) q[0];
cx q[2], q[0];
cx q[2], q[1];
rz(0.4712491131715458) q[1];
cx q[2], q[1];
rz(0.6656506840572414) q[2];
rx(1.5126955950453878) q[2];
h q[3];
cx q[0], q[3];
rz(-0.04495793256312783) q[3];
cx q[0], q[3];
... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
bit[4] c;
qubit[4] q;
h q[0];
h q[1];
h q[2];
h q[3];
cx q[2], q[0];
rz(x0) q[0];
cx q[2], q[0];
cx q[0], q[3];
rz(x1) q[3];
cx q[0], q[3];
cx... | {"source": 0, "sink": 3} | {"circuits": [], "gradients": []} | [
"IZIZ",
"ZIIZ",
"IZZI",
"ZIZI",
"IZII",
"IIIZ",
"ZIII",
"IIZI"
] | [
-1.25,
1.5,
-0.25,
-1.5,
-1.5,
-0.25,
0,
1.75
] | 0.564109 | [
0.08466080018590566,
-0.04495793256312783,
0.4712491131715458,
0.6656506840572409,
-1.5403474266364232,
-1.5490134012367487,
1.5126955950453878
] | {
"n_parameters": 7,
"n_qubits": 4,
"optimal_eigenvalue": -7.5,
"target_ratio": 0.97,
"target_value": -7.2749999999999995
} | 191 |
1d36f605f450bd24c53bed4c61ab6422 | max_flow | vqe | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"capacity": 1, "source": 0, "target": 3}, {"capacity": 2, "source": 0, "target": 4}, {"capacity": 1, "source": 1, "target": 2}, {"capacity": 2, "source": 1, "target": 6... | {"states": [49055, 47007], "expectation_value": -18.703191821109062, "params": [0.806, 0.7529, 0.027200000000000002, 0.0109, 1.0808, 1.0627, -0.7095, -0.6938000000000001, 0.46880000000000005, 0.4762, 0.7092, 0.5065000000000001, 0.6518, 0.7105, 0.8388, 0.6243000000000001, 0.7761, 0.7741, -0.0193, 0.0181, 0.0002, 0.0016,... | -0.5 * (Z(10) @ Z(3)) + -0.5 * (Z(11) @ Z(3)) + 1.0 * (Z(11) @ Z(10)) + 0.5 * (Z(4) @ Z(3)) + -0.5 * (Z(4) @ Z(10)) + -0.5 * (Z(4) @ Z(11)) + 0.5 * (Z(5) @ Z(3)) + -0.5 * (Z(5) @ Z(10)) + -0.5 * (Z(5) @ Z(11)) + 0.5 * (Z(5) @ Z(4)) + -0.5 * (Z(6) @ Z(3)) + -0.5 * (Z(7) @ Z(3)) + 1.0 * (Z(7) @ Z(6)) + -0.5 * (Z(8) @ Z(6... | 14 | 16 | 2 | {"smallest_eigenvalues": [-19.166666666666586], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -19.166666666666583, "smallest_bitstrings": ["0100100001100000"], "largest_eigenvalue": NaN} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
cx q[3], q[0];
rz(-0.44173747837386507) q[0];
cx q[3], q[0];
h q[4];
cx q[3], q[4];
rz(-0.44173747837386507) q[4];
cx q[3], q[4];
cx q[0], q[4];
rz(0.005603409297500889) q[4];
cx q[0], q[4];
cx q[4], q[2];
rz(0.005603409297500889) q[2];
c... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x100;
input float[64] x101;
input float[64] x102;
input float[64] x103;
input float[64] x104;
input float[64] x105;
input float[64] x106;
input float[64] x107;
input float[64] x108;
input float[64] x109;
i... | {"source": 0, "sink": 6} | {"circuits": [], "gradients": []} | [
"IIIIIZIIIIIIZIII",
"IIIIZIIIIIIIZIII",
"IIIIZZIIIIIIIIII",
"IIIIIIIIIIIZZIII",
"IIIIIZIIIIIZIIII",
"IIIIZIIIIIIZIIII",
"IIIIIIIIIIZIZIII",
"IIIIIZIIIIZIIIII",
"IIIIZIIIIIZIIIII",
"IIIIIIIIIIZZIIII",
"IIIIIIIIIZIIZIII",
"IIIIIIIIZIIIZIII",
"IIIIIIIIZZIIIIII",
"IIIIIIIZIZIIIIII",
"IIIIIII... | [
-0.5,
-0.5,
1,
0.5,
-0.5,
-0.5,
0.5,
-0.5,
-0.5,
0.5,
-0.5,
-0.5,
1,
-0.5,
-0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
1,
0.5,
0.5,
-0.5,
0.5,
0.5,
-0.5,
0.33333333333333337,
0.5,
0.5,
0.5,
0.5,
-0.5,
0.5,
0.5,
0.5,
0.5,
-0.5,
... | 0.970536 | [
-0.44173747837386507,
0.005603409297500889,
0.05836178307980425,
-1.201402489306377,
-0.9317048549953064,
0.7320633774444789,
0.772973794919639,
-1.6652911638748984,
-0.7518283058778058,
0.06520245980832098,
0.12228192436712314,
-0.10637680738364871,
-0.2779417698846335,
1.5718265483768925... | {
"n_parameters": 24,
"n_qubits": 7,
"optimal_eigenvalue": -6,
"target_ratio": 0.97,
"target_value": -5.82
} | 91 |
fcfd54ef615390c036c2590109c0afc6 | min_cut | vqe | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}, {"id": 10}, {"id": 11}], "edges": [{"capacity": 4, "source": 0, "target": 3}, {"capacity": 4, "source": 0, "target": 4}, {"capacity": 4, "source": ... | {"states": [2050, 2047], "expectation_value": -32.62127415627477, "params": [[[-0.0083, 1.0223], [0.0026000000000000003, -0.032100000000000004], [0.0024000000000000002, 0.0017000000000000001], [0.0029000000000000002, 0.0021000000000000003], [0.0026000000000000003, 0.0028], [0.0025, 0.0026000000000000003], [0.0028, 0.00... | -1.0 * (Z(0) @ Z(5)) + -1.75 * (Z(6) @ Z(5)) + -1.0 * (Z(6) @ Z(0)) + -0.25 * (Z(9) @ Z(5)) + -1.0 * (Z(9) @ Z(0)) + -1.5 * (Z(1) @ Z(5)) + -1.75 * (Z(1) @ Z(6)) + -0.5 * (Z(1) @ Z(9)) + -0.25 * (Z(11) @ Z(5)) + -0.25 * (Z(11) @ Z(6)) + -0.5 * (Z(11) @ Z(9)) + -2.5 * (Z(11) @ Z(1)) + -0.5 * (Z(3) @ Z(5)) + 3.25 * (Z(3)... | 15 | 12 | 3 | {"smallest_eigenvalues": [-33.25], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -32.25, "smallest_bitstrings": ["100000000000"], "largest_eigenvalue": 34.75} | OPENQASM 3.0;
include "stdgates.inc";
qubit[12] q;
ry(0.15326930737729938) q[0];
ry(0.035763430755590714) q[1];
ry(0.0070229064374921725) q[2];
ry(-0.05490340228331881) q[3];
ry(0.035763430755590714) q[4];
ry(-0.02593630851100761) q[5];
ry(-0.038464657764506846) q[6];
ry(-0.07187830044275868) q[7];
ry(-0.01080524769146... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"source": 0, "sink": 11} | {"circuits": [], "gradients": []} | [
"IIIIIIZIIIIZ",
"IIIIIZZIIIII",
"IIIIIZIIIIIZ",
"IIZIIIZIIIII",
"IIZIIIIIIIIZ",
"IIIIIIZIIIZI",
"IIIIIZIIIIZI",
"IIZIIIIIIIZI",
"ZIIIIIZIIIII",
"ZIIIIZIIIIII",
"ZIZIIIIIIIII",
"ZIIIIIIIIIZI",
"IIIIIIZIZIII",
"IIIIIIIIZIIZ",
"IIIIIZIIZIII",
"IIZIIIIIZIII",
"IIIIIIIIZIZI",
"ZIIIIIIIZ... | [
-1,
-1.75,
-1,
-0.25,
-1,
-1.5,
-1.75,
-0.5,
-0.25,
-0.25,
-0.5,
-2.5,
-0.5,
3.25,
-1.25,
-0.25,
-0.75,
-1.25,
-1.25,
-1.75,
-0.25,
-0.75,
-2.75,
-0.25,
-0.5,
-1.5,
-0.75,
-1,
-1.5,
-1.25,
-1.5,
-0.25,
-1.5,
-1,
-1.5,
3.25,
-0.25,
-1.25,
-0... | 0.97035 | [
0.15326930737729938,
0.035763430755590714,
0.0070229064374921725,
-0.05490340228331881,
-0.02593630851100761,
-0.038464657764506846,
-0.07187830044275868,
-0.010805247691465516,
-0.0006815808795822345,
0.0668476013488183,
0.11302208093083542,
1.0811506583303134,
0.04133727923987505,
0.0387... | {
"n_parameters": 40,
"n_qubits": 12,
"optimal_eigenvalue": -33.25,
"target_ratio": 0.97,
"target_value": -32.2525
} | 33 |
b99f0e315d6c4ec38babd2628ecf87b6 | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}], "edges": [{"capacity": 2, "source": 0, "target": 6}, {"capacity": 1, "source": 0, "target": 8}, {"capacity": 2, "source": 1, "target": 3}, {"capacity": 1, "s... | {"states": [67, 3], "expectation_value": -0.07877810997820567, "params": [[0.0635], [-0.0545]], "bitstrings": ["110111100", "111111100"], "total_optimization_steps": 10, "probabilities": [0.002189659683555928, 0.002204218005299875], "optimization_time": 2.207000494003296} | -0.5 * (Z(0) @ Z(6)) + 0.75 * (Z(8) @ Z(0)) + -0.25 * (Z(1) @ Z(6)) + -0.25 * (Z(3) @ Z(6)) + -0.5 * (Z(3) @ Z(1)) + -0.5 * (Z(4) @ Z(6)) + -0.25 * (Z(4) @ Z(1)) + -0.25 * (Z(5) @ Z(4)) + -0.25 * (Z(2) @ Z(5)) + -0.25 * (Z(7) @ Z(6)) + -0.25 * (Z(7) @ Z(8)) + -0.25 * (Z(7) @ Z(4)) + -0.25 * Z(6) + -0.25 * Z(0) + 0.5 * ... | 1 | 9 | 1 | {"smallest_eigenvalues": [-5.75, -5.75], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -4.75, "smallest_bitstrings": ["111111100", "110111100"], "largest_eigenvalue": 5.25} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[6], q[0];
rz(-0.6251339180222817) q[0];
cx q[6], q[0];
cx q[6], q[1];
rz(-0.3154365803553768) q[1];
cx q[6], q[1];
cx q[6], q[3];
rz(-0.3154365803553768) q[3];
cx q[6], q[3];
cx q[1], q[3];
rz(-0.6251339180222... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
bit[9] c;
qubit[9] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
h q[8];
cx q[6], q[0];
rz(x0) q[0];
cx q[6], q[0];
cx q[... | {"source": 0, "sink": 8} | {"circuits": [], "gradients": []} | [
"IIZIIIIIZ",
"ZIIIIIIIZ",
"IIZIIIIZI",
"IIZIIZIII",
"IIIIIZIZI",
"IIZIZIIII",
"IIIIZIIZI",
"IIIZZIIII",
"IIIZIIZII",
"IZZIIIIII",
"ZZIIIIIII",
"IZIIZIIII",
"IIZIIIIII",
"IIIIIIIIZ",
"ZIIIIIIII",
"IIIIIIIZI",
"IIIIIZIII",
"IIIIZIIII",
"IIIZIIIII",
"IIIIIIZII",
"IZIIIIIII"
] | [
-0.5,
0.75,
-0.25,
-0.25,
-0.5,
-0.5,
-0.25,
-0.25,
-0.25,
-0.25,
-0.25,
-0.25,
-0.25,
-0.25,
0.5,
0.5,
-0.25,
-0.75,
-0.5,
0.25,
0.75
] | 0.522241 | [
-0.6251339180222817,
0.9163473416171956,
-0.3154365803553768,
0.8098800397262919,
-1.0007381683901269,
1.2402565320189738,
-1.0128218293180618
] | {
"n_parameters": 7,
"n_qubits": 9,
"optimal_eigenvalue": -5.75,
"target_ratio": 0.97,
"target_value": -5.5775
} | 196 |
9c58c5b77a3170e613a26f379fffeef6 | matching | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"weight": 3, "source": 0, "target": 1}, {"weight": 12, "source": 0, "target": 4}, {"weight": 13, "source": 0, "target": 2}, {"weight": 18, "source": 0, "target": 5}, {"weight": 2... | {"states": [119, 118], "expectation_value": -30.558307637888625, "params": [[0.028800000000000003, 0.0028, -0.0017000000000000001], [-0.0833, -0.0765, -0.057600000000000005]], "bitstrings": ["10001000", "10001001"], "total_optimization_steps": 10, "probabilities": [0.014800796120976303, 0.018733878105929913], "optimiza... | 3.5 * (Z(0) @ Z(1)) + 3.5 * (Z(2) @ Z(1)) + 3.5 * (Z(2) @ Z(0)) + 3.5 * (Z(3) @ Z(1)) + 3.5 * (Z(3) @ Z(0)) + 3.5 * (Z(3) @ Z(2)) + 3.5 * (Z(4) @ Z(1)) + 3.5 * (Z(5) @ Z(2)) + 3.5 * (Z(5) @ Z(4)) + 3.5 * (Z(6) @ Z(3)) + 3.5 * (Z(6) @ Z(4)) + 3.5 * (Z(6) @ Z(5)) + 3.5 * (Z(7) @ Z(2)) + 3.5 * (Z(7) @ Z(3)) + 3.5 * (Z(7) ... | 1 | 8 | 3 | {"smallest_eigenvalues": [-74.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -69.0, "smallest_bitstrings": ["10001001"], "largest_eigenvalue": 158.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(-0.30035957140227065) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(-0.30035957140227065) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(-0.30035957140227065) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(-0.30035957140227065) q[3];
cx q[1], ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "perfect", "extra": "{\"n\": 6}"} | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZZI",
"IIIIIZIZ",
"IIIIZIZI",
"IIIIZIIZ",
"IIIIZZII",
"IIIZIIZI",
"IIZIIZII",
"IIZZIIII",
"IZIIZIII",
"IZIZIIII",
"IZZIIIII",
"ZIIIIZII",
"ZIIIZIII",
"ZIZIIIII",
"ZZIIIIII",
"IIIIIIZI",
"IIIIIIIZ",
"IIIIIZII",
"IIIIZIII",
"IIIZIIII",
"IIZIIIII",
"IZIIIII... | [
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
3.5,
13.5,
5,
16.5,
19.5,
4.5,
17,
14.5,
11.5
] | 0.970623 | [
-0.30035957140227065,
1.1368758079646883,
-1.8923990284899774,
1.0436850348571591,
1.415620980349364,
-0.5091827167950427,
1.4790986719477293,
0.8820371628830349,
0.46473221419256594,
-0.15090594742638722,
0.055618018346008394,
0.32882508347878925,
-0.3312498441524585,
-0.09748772199396417... | {
"n_parameters": 30,
"n_qubits": 8,
"optimal_eigenvalue": -74,
"target_ratio": 0.97,
"target_value": -71.78
} | 54 |
-3942045383418848897 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7], "hyperedges": [[6, 7], [0, 2, 3, 7], [0, 2, 3, 4], [1, 2, 4, 5], [2, 4, 5, 6]]} | {"states": [222, 246], "expectation_value": -0.7286730128817186, "params": [[0.4665], [-0.4456]], "bitstrings": ["00100001", "00001001"], "total_optimization_steps": 50, "probabilities": [0.011516565897959564, 0.011734151475322505], "optimization_time": 3.093832492828369} | 0.5 * (Z(6) @ Z(7)) + 0.08333333333333333 * (Z(0) @ Z(7)) + 0.08333333333333333 * (Z(2) @ Z(7)) + 0.08333333333333333 * (Z(2) @ Z(6)) + 0.16666666666666666 * (Z(2) @ Z(0)) + 0.08333333333333333 * (Z(3) @ Z(7)) + 0.16666666666666666 * (Z(3) @ Z(0)) + 0.16666666666666666 * (Z(3) @ Z(2)) + 0.08333333333333333 * (Z(4) @ Z(... | 1 | 8 | 1 | {"smallest_eigenvalues": [-1.5, -1.5, -1.5], "number_of_smallest_eigenvalues": 3, "first_excited_energy": -1.416666666666667, "smallest_bitstrings": ["01010010", "11000010", "00001001"], "largest_eigenvalue": 4.500000000000001} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
cx q[7], q[6];
rz(1.4696369217647303) q[6];
cx q[7], q[6];
cx q[7], q[0];
rz(0.08802784627789033) q[0];
cx q[7], q[0];
cx q[7], q[2];
rz(0.08802784627789033) q[2];
cx q[7], q[2];
cx q[6], q[2];
rz(0.0880278... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
bit[8] c;
qubit[8] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
cx q[7], q[6];
rz(x0) q[6];
cx q[7],... | null | {"circuits": [], "gradients": []} | [
"ZZIIIIII",
"ZIIIIIIZ",
"ZIIIIZII",
"IZIIIZII",
"IIIIIZIZ",
"ZIIIZIII",
"IIIIZIIZ",
"IIIIZZII",
"IZIZIIII",
"IIIZIIIZ",
"IIIZIZII",
"IIIZZIII",
"IIIIIZZI",
"IIIZIIZI",
"IZZIIIII",
"IIZIIZII",
"IIZZIIII",
"IIZIIIZI",
"ZIIIIIII",
"IZIIIIII",
"IIIIIIIZ",
"IIIIIZII",
"IIIIZII... | [
0.5,
0.08333333333333333,
0.08333333333333333,
0.08333333333333333,
0.16666666666666666,
0.08333333333333333,
0.16666666666666666,
0.16666666666666666,
0.08333333333333333,
0.08333333333333333,
0.25,
0.08333333333333333,
0.08333333333333333,
0.08333333333333333,
0.08333333333333333,
0.... | 0.765104 | [
1.4696369217647303,
0.08802784627789033,
0.36357790409071217,
0.056575741642996384,
0.003492892383003796,
0.3659192124632948,
1.193856197536988,
-0.8436888665698518
] | {
"n_parameters": 8,
"n_qubits": 8,
"optimal_eigenvalue": -1.5,
"target_ratio": 0.97,
"target_value": -1.455
} | 201 |
a887d91f9606dc8ffadccd46fa1ed57b | min_cut | vqe | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"capacity": 6, "source": 0, "target": 2}, {"capacity": 5, "source": 0, "target": 3}, {"capacity": 6, "source": 0, "target": 5}, {"capacity": 2, "source": 1, "target": 2}, {"capaci... | {"states": [1, 17], "expectation_value": -6.954915365150812, "params": [[[0.0004, 0.3356], [0.5891000000000001, 0.003], [0.0035, 0.4339], [0.0051, 0.2082], [0.0012000000000000001, 0.4576], [0.603, 0.0031000000000000003]], [[0.0033, 0.37270000000000003], [0.5933, 0.003], [-0.0001, 0.2919], [0.0008, 0.3584], [0.0061, 0.4... | -1.5 * (Z(0) @ Z(2)) + -1.25 * (Z(3) @ Z(0)) + 3.0 * (Z(5) @ Z(0)) + -1.0 * (Z(5) @ Z(3)) + -0.5 * (Z(1) @ Z(2)) + -0.5 * (Z(1) @ Z(5)) + -0.75 * (Z(4) @ Z(3)) + -2.0 * Z(2) + -0.25 * Z(0) + 0.5 * Z(3) + 1.5 * Z(5) + 1.0 * Z(1) + -0.75 * Z(4) | 1 | 6 | 3 | {"smallest_eigenvalues": [-10.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -9.5, "smallest_bitstrings": ["101110"], "largest_eigenvalue": 10.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
rz(-2.7026747242885296) q[0];
ry(0.04369070613606717) q[0];
rz(-2.3989077382019692) q[0];
rz(1.2390313594475595) q[1];
ry(2.7029776244779247) q[1];
rz(-1.8931095271762974) q[1];
rz(1.2296356242845414) q[2];
ry(0.07252810464454057) q[2];
rz(-0.8196100966248716) q[2];
rz(... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"source": 0, "sink": 5} | {"circuits": [], "gradients": []} | [
"IIIZIZ",
"IIZIIZ",
"ZIIIIZ",
"ZIZIII",
"IIIZZI",
"ZIIIZI",
"IZZIII",
"IIIZII",
"IIIIIZ",
"IIZIII",
"ZIIIII",
"IIIIZI",
"IZIIII"
] | [
-1.5,
-1.25,
3,
-1,
-0.5,
-0.5,
-0.75,
-2,
-0.25,
0.5,
1.5,
1,
-0.75
] | 0.983616 | [
-0.10851937358898682,
0.4487744318096143,
1.03540924260132,
-0.08402551519855138,
0.11521988296733376,
0.42557088328310494,
-0.050850343758797184,
0.2581494561174059,
-0.14082975527251856,
0.5348791684932794,
0.6541134772230921,
-0.015841090960918423,
0.10336452295257065,
0.568926069772383... | {
"n_parameters": 34,
"n_qubits": 6,
"optimal_eigenvalue": -10.5,
"target_ratio": 0.97,
"target_value": -10.185
} | 11 |
6a865e73d4e6861d0009457718f7c0e7 | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 1, "target": 4}, ... | {"states": [4606, 12798], "expectation_value": -2.8332196218312875, "params": [0.8399000000000001, 0.0753, 1.1062, 0.0166, 0.32320000000000004, 0.4621, 0.2822, -0.4988, 0.35350000000000004, 0.46590000000000004, 1.0949, -0.0358, 1.0704, -0.0051, 1.0491000000000001, -0.0038, 1.0626, -0.0037, 1.0719, -0.001700000000000000... | 0.25 * (Z(0) @ Z(1)) + 0.25 * (Z(0) @ Z(2)) + 0.25 * (Z(1) @ Z(2)) + -0.25 * (Z(0) @ Z(1) @ Z(2)) + 0.25 * (Z(3) @ Z(4)) + 0.25 * (Z(3) @ Z(5)) + 0.25 * (Z(4) @ Z(5)) + -0.25 * (Z(3) @ Z(4) @ Z(5)) + 0.03125 * (Z(0) @ Z(3)) + 0.03125 * (Z(6) @ Z(0)) + 0.03125 * (Z(0) @ Z(7)) + 0.03125 * (Z(0) @ Z(8)) + 0.03125 * (Z(0) ... | 4 | 14 | 2 | {"smallest_eigenvalues": [-4.093750000000002], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -4.09375, "smallest_bitstrings": ["00111000000001"], "largest_eigenvalue": 5.90625} | OPENQASM 3.0;
include "stdgates.inc";
qubit[14] q;
rx(1.052767296367402) q[0];
rz(1.734067282606989) q[0];
rx(1.482795815494667) q[1];
rz(1.7017603609172856) q[1];
rx(0.0068950644822173834) q[2];
rz(2.098322727352551) q[2];
rx(-0.016557334720073695) q[3];
rz(0.9175952001748406) q[3];
rx(0.08624653593471021) q[4];
rz(2.... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIIIIIIZZ",
"IIIIIIIIIIIZIZ",
"IIIIIIIIIIIZZI",
"IIIIIIIIIIIZZZ",
"IIIIIIIIIZZIII",
"IIIIIIIIZIZIII",
"IIIIIIIIZZIIII",
"IIIIIIIIZZZIII",
"IIIIIIIIIIZIIZ",
"IIIIIIIZIIIIIZ",
"IIIIIIZIIIIIIZ",
"IIIIIZIIIIIIIZ",
"IIIIZIIIIIIIIZ",
"IIIIIIIZIIZIII",
"IIIIIIZIIIZIII",
"IIIIIZIIIIZIII"... | [
0.25,
0.25,
0.25,
-0.25,
0.25,
0.25,
0.25,
-0.25,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
0.03125,
-0.03125,
-0.03125,
-0.03125,
-0.03125,
-0.03125,
-0.03125,
-0.03125,
-... | 0.970859 | [
1.0527672963674022,
0.16327095581209236,
1.482795815494667,
0.13096403412238927,
0.0068950644822173834,
0.5275264005576541,
-0.016557334720073695,
-0.6532011266200554,
0.08624653593471021,
0.5244226051858115,
1.0723714721411683,
0.022999901950381763,
1.2208840667300707,
-0.1541568350571987... | {
"n_parameters": 80,
"n_qubits": 14,
"optimal_eigenvalue": -4.093750000000002,
"target_ratio": 0.97,
"target_value": -3.9709375000000016
} | 21 |
85892c11b8f43dcff24467d969952465 | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 0, "id": 3}, {"bipartite": 0, "id": 4}, {"bipartite": 0, "id": 5}, {"bipartite": 0, "id": 6}, {"bipartite": 1, "id": 7}, {"bipartite": 1, "id": 8}, {"bipartite":... | {"states": [711, 199], "expectation_value": -73.4182494123019, "params": [0.7317, 0.2523, 0.4842, 0.3433, 1.2014, 0.0171, 1.2012, -0.15410000000000001, 0.5672, -0.2461, 0.0034000000000000002, 0.6224000000000001, 0.0025, 0.8563000000000001, 1.201, 0.0045000000000000005, 1.208, -0.001, 1.204, 0.045000000000000005, 0.7344... | 6.5 * (Z(0) @ Z(2)) + 6.5 * (Z(4) @ Z(2)) + 6.5 * (Z(3) @ Z(2)) + 6.5 * (Z(3) @ Z(4)) + 6.5 * (Z(1) @ Z(3)) + 6.5 * (Z(7) @ Z(2)) + 6.5 * (Z(7) @ Z(0)) + 6.5 * (Z(9) @ Z(3)) + 6.5 * (Z(9) @ Z(1)) + 6.5 * (Z(8) @ Z(9)) + 6.5 * (Z(5) @ Z(8)) + 23.0 * Z(2) + 4.0 * Z(0) + 2.0 * Z(4) + 21.0 * Z(3) + 1.0 * Z(1) + 10.0 * Z(7)... | 18 | 10 | 2 | {"smallest_eigenvalues": [-106.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -94.0, "smallest_bitstrings": ["1100111000"], "largest_eigenvalue": 165.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
rx(0.17514785949857475) q[0];
rz(0.5443196683222373) q[0];
rx(0.019332298552619004) q[1];
rz(0.3655516039630416) q[1];
rx(1.4207135528670727) q[2];
rz(-0.02465751539851134) q[2];
rx(1.6381477226469006) q[3];
rz(-0.24195124357252715) q[3];
rx(0.2141283348221449) q[4];
r... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum_bipartite", "extra": "{\"left_nodes\": [0, 1, 2, 3, 4, 5, 6], \"right_nodes\": [7, 8, 9, 10, 11]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIZIZ",
"IIIIIZIZII",
"IIIIIIZZII",
"IIIIIZZIII",
"IIIIIIZIZI",
"IIZIIIIZII",
"IIZIIIIIIZ",
"ZIIIIIZIII",
"ZIIIIIIIZI",
"ZZIIIIIIII",
"IZIIZIIIII",
"IIIIIIIZII",
"IIIIIIIIIZ",
"IIIIIZIIII",
"IIIIIIZIII",
"IIIIIIIIZI",
"IIZIIIIIII",
"ZIIIIIIIII",
"IZIIIIIIII",
"IIIIZIIIII"... | [
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
6.5,
23,
4,
2,
21,
1,
10,
14.5,
9,
-3.5,
-12.5
] | 0.976944 | [
0.17514785949857473,
0.3761700515815528,
0.019332298552619004,
0.3655516039630416,
1.4207135528670727,
-0.02465751539851134,
1.6381477226469006,
-0.24195124357252715,
0.2141283348221449,
-0.3339414315172169,
0.05762316749730125,
0.49515307029904027,
-0.21341772442398688,
0.9515120285488028... | {
"n_parameters": 56,
"n_qubits": 10,
"optimal_eigenvalue": -106,
"target_ratio": 0.97,
"target_value": -102.82
} | 16 |
9915ff93784d747e82bcd9a73a2399e5 | kclique | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 4}, {"id": 5}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 4}, {"source": 0, "target": 5}, {"source": 1, "target": 2}]} | {"states": [9, 3], "expectation_value": -7.275005931388309, "params": null, "bitstrings": ["10110", "11100"], "total_optimization_steps": 29, "probabilities": [0.12631059505875555, 0.6745310886168708], "optimization_time": 29.945663690567017} | 1.75 * (Z(0) @ Z(1)) + 1.75 * (Z(2) @ Z(1)) + 1.75 * (Z(2) @ Z(0)) + 2.0 * (Z(3) @ Z(1)) + 1.75 * (Z(3) @ Z(0)) + 2.0 * (Z(3) @ Z(2)) + 2.0 * (Z(4) @ Z(1)) + 1.75 * (Z(4) @ Z(0)) + 2.0 * (Z(4) @ Z(2)) + 2.0 * (Z(4) @ Z(3)) + -2.5 * Z(1) + -3.0 * Z(0) + -2.5 * Z(2) + -2.25 * Z(3) + -2.25 * Z(4) | 11 | 5 | 4 | {"smallest_eigenvalues": [-7.75], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -6.75, "smallest_bitstrings": ["11100"], "largest_eigenvalue": 31.25} | OPENQASM 3.0;
include "stdgates.inc";
qubit[5] q;
rz(-pi) q[0];
ry(-0.0251969072812812) q[0];
h q[1];
ry(-0.5380823333224228) q[1];
h q[2];
ry(-0.5380823333224228) q[2];
h q[3];
cx q[3], q[1];
ry(0.5380823333224228) q[1];
cx q[3], q[1];
ry(-0.8810269947366784) q[1];
ry(1.3888852652990713) q[3];
h q[4];
cx q[4], q[2];
r... | null | {"k": 3} | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[5] c;\nqubit[5] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nry(-1.5709) q[0];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\n", "OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[5] c;\nqubit[5]... | [
"IIIZZ",
"IIZZI",
"IIZIZ",
"IZIZI",
"IZIIZ",
"IZZII",
"ZIIZI",
"ZIIIZ",
"ZIZII",
"ZZIII",
"IIIZI",
"IIIIZ",
"IIZII",
"IZIII",
"ZIIII"
] | [
1.75,
1.75,
1.75,
2,
1.75,
2,
2,
1.75,
2,
2,
-2.5,
-3,
-2.5,
-2.25,
-2.25
] | 0.972771 | [
-1.7357936832727832,
-1.0761646666448457,
0.8318258295933451,
1.3888852652990713,
-0.5583266175622739,
-0.9112528734271876,
0.7301946700289301,
-0.2369592768426538,
0.13507114255148295,
0.06045175738101835,
0.5736330844182135,
0.4348793797484596,
-0.5033799150929571,
-0.6485481651535171,
... | {
"n_parameters": 17,
"n_qubits": 5,
"optimal_eigenvalue": -7.75,
"target_ratio": 0.97,
"target_value": -7.5175
} | 14 |
4c48a0bc3d9383f39c57939a9b280334 | vertex_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 5}, {"source": 0, "target": 8}, {"source": 1, "target": 4}, {"source": 1, "target": 5}, {"sour... | {"states": [81, 89], "expectation_value": -6.555349184261167, "params": [[0.0014, -0.0044, 1.0427, -0.002, 1.5694000000000001, 0.6604, 0.003, 0.1892, 1.5838], [-0.0035, -0.0016, 1.0483, -0.0024000000000000002, 0.9049, -0.6651, 0.003, 0.2918, 1.56], [0.0034000000000000002, -0.0016, 1.0441, -0.0022, 0.8969, 0.8023, 0.003... | 0.5 * (Z(0) @ Z(2)) + 0.5 * (Z(5) @ Z(0)) + 0.5 * (Z(8) @ Z(0)) + 0.5 * (Z(1) @ Z(5)) + 0.5 * (Z(1) @ Z(8)) + 0.5 * (Z(4) @ Z(1)) + 0.5 * (Z(6) @ Z(1)) + 0.5 * (Z(6) @ Z(4)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(3) @ Z(8)) + 0.5 * (Z(3) @ Z(4)) + 0.5 * (Z(3) @ Z(6)) + 0.5 * (Z(7) @ Z(5)) + 0.5 * (Z(7) @ Z(8)) + 0.5 * (Z(7) ... | 10 | 9 | 2 | {"smallest_eigenvalues": [-7.0, -7.0], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -6.0, "smallest_bitstrings": ["110100110", "110110010"], "largest_eigenvalue": 18.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
ry(0.1548645880780616) q[0];
ry(-0.04456629720004046) q[1];
ry(1.0438142037297182) q[2];
ry(-0.03441010696231078) q[3];
ry(1.816337516419338) q[4];
ry(0.7918044141493651) q[5];
ry(-0.08387749623534291) q[6];
ry(0.11730790537756046) q[7];
ry(1.5950285833424724) q[8];
cz ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZIZ",
"IIIZIIIIZ",
"ZIIIIIIIZ",
"IIIZIIIZI",
"ZIIIIIIZI",
"IIIIZIIZI",
"IIZIIIIZI",
"IIZIZIIII",
"IIIIIZZII",
"ZIIIIZIII",
"IIIIZZIII",
"IIZIIZIII",
"IZIZIIIII",
"ZZIIIIIII",
"IZIIIZIII",
"IIIIIIZII",
"IIIIIIIIZ",
"IIIZIIIII",
"ZIIIIIIII",
"IIIIIIIZI",
"IIIIZIIII",
"... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-0.5,
-1,
-1,
-1.5,
-1.5,
-1,
-1,
-2,
-1
] | 0.976847 | [
0.1548645880780616,
-0.04456629720004046,
1.0438142037297182,
-0.03441010696231078,
1.816337516419338,
0.7918044141493651,
-0.08387749623534291,
0.11730790537756046,
1.5950285833424724,
-0.21222370140366575,
-0.061429974068226825,
1.2535663545400582,
-0.02596174819668317,
1.049682785587165... | {
"n_parameters": 25,
"n_qubits": 9,
"optimal_eigenvalue": -7,
"target_ratio": 0.97,
"target_value": -6.79
} | 6 |
6484834437226800471 | hypermaxcut | adaptive_vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7], "hyperedges": [[1, 2, 4, 6, 7], [0, 5], [3, 5]]} | {"states": [219, 155], "expectation_value": -1.0078272624619007, "params": null, "bitstrings": ["00100100", "01100100"], "total_optimization_steps": 57, "probabilities": [0.14032362325037823, 0.1520475802572063], "optimization_time": 69.84665250778198} | 0.05 * (Z(1) @ Z(2)) + 0.05 * (Z(4) @ Z(2)) + 0.05 * (Z(4) @ Z(1)) + 0.05 * (Z(6) @ Z(2)) + 0.05 * (Z(6) @ Z(1)) + 0.05 * (Z(6) @ Z(4)) + 0.05 * (Z(7) @ Z(2)) + 0.05 * (Z(7) @ Z(1)) + 0.05 * (Z(7) @ Z(4)) + 0.05 * (Z(7) @ Z(6)) + 0.5 * (Z(0) @ Z(5)) + 0.5 * (Z(3) @ Z(5)) + 0.1 * Z(2) + 0.1 * Z(1) + 0.1 * Z(4) + 0.1 * Z... | 1 | 8 | 1 | {"smallest_eigenvalues": [-1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, -1.2000000000000002, ... | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
h q[0];
h q[1];
h q[2];
ry(-0.5137422452837753) q[2];
cx q[1], q[2];
ry(0.5137422452837753) q[2];
cx q[1], q[2];
ry(-0.10065700764097371) q[1];
cx q[2], q[1];
ry(0.10065700764097371) q[1];
cx q[2], q[1];
ry(-0.07001195282108426) q[2];
ry(-0.002155238839234304) q[1];
h q... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[8] c;\nqubit[8] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\ncry(-1.0342) q[3], q[5];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = me... | [
"IIIIIZZI",
"IIIZIZII",
"IIIZIIZI",
"IZIIIZII",
"IZIIIIZI",
"IZIZIIII",
"ZIIIIZII",
"ZIIIIIZI",
"ZIIZIIII",
"ZZIIIIII",
"IIZIIIIZ",
"IIZIZIII",
"IIIIIZII",
"IIIIIIZI",
"IIIZIIII",
"IZIIIIII",
"ZIIIIIII",
"IIZIIIII",
"IIIIIIIZ",
"IIIIZIII"
] | [
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.05,
0.5,
0.5,
0.1,
0.1,
0.1,
0.1,
0.1,
0,
0,
0
] | 0.972062 | [
-0.9832364975404541,
1.3755127073122557,
-0.5647184777909868,
1.3753502448397068,
0.21800111152446866,
-0.46948279537947835,
0.1951253207951374,
0.7054255721930438,
0.7775150377300192,
-0.6400278384153306,
0.019393846482221783,
0.17163633887674756,
0.26186488771334987,
-0.5220012047021363,... | {
"n_parameters": 51,
"n_qubits": 8,
"optimal_eigenvalue": -1.2000000000000002,
"target_ratio": 0.97,
"target_value": -1.1640000000000001
} | 18 |
-5606904408919019912 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6], "hyperedges": [[1, 4, 5], [0, 1, 6], [4, 6], [3, 5, 6], [1, 3], [0, 1, 2, 5]]} | {"states": [35, 51], "expectation_value": -0.46053050061227857, "params": [[-0.2431], [0.2524]], "bitstrings": ["1011100", "1001100"], "total_optimization_steps": 30, "probabilities": [0.015408505059725384, 0.015578014613635312], "optimization_time": 1.7582452297210693} | 0.16666666666666666 * (Z(1) @ Z(4)) + 0.16666666666666666 * (Z(5) @ Z(4)) + 0.25 * (Z(5) @ Z(1)) + 0.25 * (Z(0) @ Z(1)) + 0.08333333333333333 * (Z(0) @ Z(5)) + 0.5 * (Z(6) @ Z(4)) + 0.16666666666666666 * (Z(6) @ Z(1)) + 0.16666666666666666 * (Z(6) @ Z(5)) + 0.16666666666666666 * (Z(6) @ Z(0)) + 0.5 * (Z(3) @ Z(1)) + 0.... | 1 | 7 | 1 | {"smallest_eigenvalues": [-2.25], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.1666666666666665, "smallest_bitstrings": ["1001100"], "largest_eigenvalue": 5.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
cx q[4], q[1];
rz(0.04671223059259256) q[1];
cx q[4], q[1];
h q[5];
cx q[4], q[5];
rz(0.04671223059259256) q[5];
cx q[4], q[5];
cx q[1], q[5];
rz(-0.052667827991550176) q[5];
cx q[1], q[5];
cx q[1], q[0];
rz(-0.052667827991550176)... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
bit[7] c;
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[4], q[1];
rz(x0) q[... | null | {"circuits": [], "gradients": []} | [
"IIZIIZI",
"IZZIIII",
"IZIIIZI",
"IIIIIZZ",
"IZIIIIZ",
"ZIZIIII",
"ZIIIIZI",
"ZZIIIII",
"ZIIIIIZ",
"IIIZIZI",
"IZIZIII",
"ZIIZIII",
"IIIIZZI",
"IZIIZII",
"IIIIZIZ",
"IIZIIII",
"IIIIIZI",
"IZIIIII",
"IIIIIIZ",
"ZIIIIII",
"IIIZIII",
"IIIIZII"
] | [
0.16666666666666666,
0.16666666666666666,
0.25,
0.25,
0.08333333333333333,
0.5,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.16666666666666666,
0.16666666666666666,
0.08333333333333333,
0.08333333333333333,
0.08333333333333333,
0.16666666666666663,
0.45833333... | 0.61147 | [
0.04671223059259256,
-0.052667827991550176,
-0.14042034910600307,
-1.5204759966312231,
-0.8273005296593096,
-1.4937560825278697,
-0.0719327010352439,
-0.5227796191779338,
0.873077708657223
] | {
"n_parameters": 9,
"n_qubits": 7,
"optimal_eigenvalue": -2.25,
"target_ratio": 0.97,
"target_value": -2.1825
} | 236 |
18eef7556e7c99f2056daf5370482c12 | matching | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}], "edges": [{"weight": 2, "source": 0, "target": 1}, {"weight": 12, "source": 0, "target": 3}, {"weight": 20, "source": 0, "target": 5}, {"weight": 18, "source": 1, "tar... | {"states": [202, 234], "expectation_value": -42.98247639219426, "params": null, "bitstrings": ["100110101", "100010101"], "total_optimization_steps": 100, "probabilities": [0.17712296465766092, 0.21581777408593364], "optimization_time": 206.91220378875732} | 4.5 * (Z(0) @ Z(1)) + 4.5 * (Z(2) @ Z(1)) + 4.5 * (Z(2) @ Z(0)) + 4.5 * (Z(3) @ Z(0)) + 4.5 * (Z(3) @ Z(2)) + 4.5 * (Z(4) @ Z(1)) + 4.5 * (Z(5) @ Z(1)) + 4.5 * (Z(5) @ Z(2)) + 4.5 * (Z(5) @ Z(3)) + 4.5 * (Z(5) @ Z(4)) + 4.5 * (Z(6) @ Z(2)) + 4.5 * (Z(6) @ Z(3)) + 4.5 * (Z(6) @ Z(5)) + 4.5 * (Z(7) @ Z(6)) + 4.5 * (Z(8) ... | 1 | 9 | 3 | {"smallest_eigenvalues": [-89.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -79.0, "smallest_bitstrings": ["100010101"], "largest_eigenvalue": 170.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
ry(-1.910725201830011) q[0];
rz(-pi) q[0];
h q[1];
ry(14.226814631084332) q[1];
rz(-pi) q[2];
ry(-2.8276055261302573) q[2];
rz(-pi) q[3];
ry(-0.6037335772354969) q[3];
h q[4];
ry(-2.503200618475903) q[5];
rz(-pi) q[5];
cx q[1], q[5];
ry(-0.634351839760383) q[5];
cx q[1]... | null | {"matching": "perfect", "extra": "{\"n\": 8}"} | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[9] c;\nqubit[9] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\nh q[8];\nry(23.9941) q[2];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = ... | [
"IIIIIIIZZ",
"IIIIIIZZI",
"IIIIIIZIZ",
"IIIIIZIIZ",
"IIIIIZZII",
"IIIIZIIZI",
"IIIZIIIZI",
"IIIZIIZII",
"IIIZIZIII",
"IIIZZIIII",
"IIZIIIZII",
"IIZIIZIII",
"IIZZIIIII",
"IZZIIIIII",
"ZZIIIIIII",
"IIIIIIIZI",
"IIIIIIIIZ",
"IIIIIIZII",
"IIIIIZIII",
"IIIIZIIII",
"IIIZIIIII",
"... | [
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
4.5,
15,
5.5,
23.5,
18,
0.5,
22.5,
13,
5.5,
-1
] | 0.972353 | [
23.579116185633968,
63.12990552371649,
12.80359732253481,
14.226814631084332,
1.268703679520766,
-17.389883838771233,
4.50366295300341,
0.28630146122490274,
2.0891079396670342,
-41.664855259309064,
-18.144190662538225,
50.08291549902295,
-0.7897217290145451,
6.876816994677622,
49.5161117... | {
"n_parameters": 80,
"n_qubits": 9,
"optimal_eigenvalue": -89,
"target_ratio": 0.97,
"target_value": -86.33
} | 104 |
ebed2b2f1ddd19051c3f8f1e6db408b8 | graph_isomorphism | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}], "edges": []} | {"states": [443, 427], "expectation_value": -3.04630781205157, "params": [2.6756, 0.006200000000000001, 2.6095, 0.003, 1.5068000000000001, 0.0027, 2.3423000000000003, 0.0081, 1.5334, 0.0039000000000000003, 2.6677, 0.0034000000000000002, 1.5171000000000001, 0.0037, 2.6447000000000003, 0.0014, 2.6341, 0.0047, 0.008, 0.00... | 0.5 * (Z(0) @ Z(2)) + 0.5 * (Z(1) @ Z(2)) + 0.5 * (Z(1) @ Z(0)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(5) @ Z(2)) + 0.5 * (Z(5) @ Z(3)) + 0.5 * (Z(4) @ Z(1)) + 0.5 * (Z(4) @ Z(3)) + 0.5 * (Z(4) @ Z(5)) + 0.5 * (Z(6) @ Z(0)) + 0.5 * (Z(6) @ Z(3)) + 0.5 * (Z(8) @ Z(2)) + 0.5 * (Z(8) @ Z(5)) + 0.5 * (Z(8) @ Z(6)) + 0.5 * (Z(7) ... | 18 | 9 | 1 | {"smallest_eigenvalues": [-6.0, -6.0, -6.0, -6.0, -6.0, -6.0], "number_of_smallest_eigenvalues": 6, "first_excited_energy": -4.0, "smallest_bitstrings": ["001010100", "001100010", "010001100", "010100001", "100010001", "100001010"], "largest_eigenvalue": 18.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
rx(-2.815869706397565) q[0];
rz(-0.10266699916250133) q[0];
rx(2.938411203352395) q[1];
rz(-0.359908355829058) q[1];
rx(-0.027903752025837614) q[2];
rz(0.2181567296090501) q[2];
rx(3.0078051915562813) q[3];
rz(0.18559254664400454) q[3];
rx(0.33346172350010733) q[4];
rz(... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"autoisomorphic_graph": {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 2}, {"id": 1}], "edges": []}} | {"circuits": [], "gradients": []} | [
"IIIIIIZIZ",
"IIIIIIZZI",
"IIIIIIIZZ",
"IIIIIZIIZ",
"IIIZIIZII",
"IIIZIZIII",
"IIIIZIIZI",
"IIIIZZIII",
"IIIZZIIII",
"IIZIIIIIZ",
"IIZIIZIII",
"ZIIIIIZII",
"ZIIZIIIII",
"ZIZIIIIII",
"IZIIIIIZI",
"IZIIZIIII",
"IZZIIIIII",
"ZZIIIIIII",
"IIIIIIZII",
"IIIIIIIIZ",
"IIIIIIIZI",
"... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
1,
1,
1,
1,
1,
1,
1,
1,
1
] | 0.97428 | [
3.467315600782021,
-0.08758761771970738,
2.938411203352395,
-0.359908355829058,
-0.027903752025837614,
0.2181567296090501,
3.0078051915562813,
0.18559254664400454,
0.33346172350010733,
0.007502932029881421,
3.1040264026485866,
0.08178816583284416,
0.10051399472175349,
-0.3883946671857684,
... | {
"n_parameters": 26,
"n_qubits": 9,
"optimal_eigenvalue": -6,
"target_ratio": 0.97,
"target_value": -5.82
} | 19 |
5894180811578217904 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], "hyperedges": [[0, 1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 3, 5, 6, 8, 9], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10], [0, 1, 2, 4, 5, 6, 7, 8, 9, 10], [0, 1, 2, 3, 4, 5, 6, 7, 8, 10], [0, 1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 5, 6, 7, 9, 10]]} | {"states": [923, 1947], "expectation_value": -1.1380928535687984, "params": [0.9037000000000001, -0.3884, 0.8976000000000001, 0.0002, 1.3323, -0.1686, 1.7646000000000002, 0.0059, 1.5712000000000002, 0.0019, 1.5644, 0.0027, 1.5734000000000001, -0.0036000000000000003, 1.5715000000000001, 0.006900000000000001, 0.2877, -0.... | 0.05119047619047619 * (Z(0) @ Z(1)) + 0.06507936507936507 * (Z(2) @ Z(1)) + 0.0623015873015873 * (Z(2) @ Z(0)) + 0.0873015873015873 * (Z(3) @ Z(1)) + 0.05119047619047619 * (Z(3) @ Z(0)) + 0.06507936507936507 * (Z(3) @ Z(2)) + 0.06507936507936507 * (Z(4) @ Z(1)) + 0.0623015873015873 * (Z(4) @ Z(0)) + 0.0761904761904762 ... | 7 | 11 | 1 | {"smallest_eigenvalues": [-1.2119047619047625, -1.2119047619047625], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -1.2007936507936519, "smallest_bitstrings": ["00001100100", "00100100100"], "largest_eigenvalue": 7.000000000000003} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
rx(1.0904811725740076) q[0];
rz(-0.31745544303223827) q[0];
rx(1.291994148182073) q[1];
rz(-0.2601102474068078) q[1];
cx q[1], q[0];
rz(0.14828792694066625) q[0];
cx q[1], q[0];
rx(1.3964449821386875) q[0];
rz(-0.022022129225798666) q[0];
rx(1.739344305385593) q[1];
rz... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIIIZZ",
"IIIIIIIIZZI",
"IIIIIIIIZIZ",
"IIIIIIIZIZI",
"IIIIIIIZIIZ",
"IIIIIIIZZII",
"IIIIIIZIIZI",
"IIIIIIZIIIZ",
"IIIIIIZIZII",
"IIIIIIZZIII",
"IIIIIZIIIZI",
"IIIIIZIIIIZ",
"IIIIIZIIZII",
"IIIIIZIZIII",
"IIIIIZZIIII",
"IIIZIIIIIZI",
"IIIZIIIIIIZ",
"IIIZIIIIZII",
"IIIZIIIZI... | [
0.05119047619047619,
0.06507936507936507,
0.0623015873015873,
0.0873015873015873,
0.05119047619047619,
0.06507936507936507,
0.06507936507936507,
0.0623015873015873,
0.0761904761904762,
0.06507936507936507,
0.08055555555555555,
0.044444444444444446,
0.058333333333333334,
0.08055555555555555... | 0.970409 | [
1.0904811725740078,
-0.16916751609157185,
1.291994148182073,
-0.2601102474068078,
1.5141863963307691,
0.036380551024096104,
1.5367837817983527,
-0.22513440378638788,
0.2209480468041039,
-0.9290714700816798,
0.02787066064221791,
-1.0560194725147969,
1.3248384854659283,
0.01518785760976247,
... | {
"n_parameters": 52,
"n_qubits": 11,
"optimal_eigenvalue": -1.2119047619047625,
"target_ratio": 0.97,
"target_value": -1.1755476190476195
} | 7 |
4148495353850005104 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], "hyperedges": [[9, 6], [1, 3], [0, 3], [0, 1], [2, 3], [9, 3], [3, 7], [4, 7], [6, 7], [8, 1], [0, 9], [2, 5], [4, 6], [9, 4], [9, 7], [8, 3], [1, 6], [3, 5], [5, 6], [4, 5], [0, 4], [2, 7], [3, 4]]} | {"states": [235, 234], "expectation_value": -3.9611299303435623, "params": [0.447, -0.0603, 0.0027, 0.001, 1.5082, 1.6271, 1.5832000000000002, 1.5542, 1.7348000000000001, 1.3964, -0.22940000000000002, 0.2238, 1.5644, 1.5808, -0.0031000000000000003, 0.0, 1.3332000000000002, 1.8114000000000001, 0.8442000000000001, 0.7721... | 0.5 * (Z(9) @ Z(6)) + 0.5 * (Z(1) @ Z(6)) + 0.5 * (Z(3) @ Z(9)) + 0.5 * (Z(3) @ Z(1)) + 0.5 * (Z(0) @ Z(9)) + 0.5 * (Z(0) @ Z(1)) + 0.5 * (Z(0) @ Z(3)) + 0.5 * (Z(2) @ Z(3)) + 0.5 * (Z(7) @ Z(6)) + 0.5 * (Z(7) @ Z(9)) + 0.5 * (Z(7) @ Z(3)) + 0.5 * (Z(7) @ Z(2)) + 0.5 * (Z(4) @ Z(6)) + 0.5 * (Z(4) @ Z(9)) + 0.5 * (Z(4) ... | 14 | 10 | 1 | {"smallest_eigenvalues": [-4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5, -4.5], "number_of_smallest_eigenvalues": 26, "first_excited_energy": -3.5, "smallest_bitstrings": ["1011101010", "1010101010", "0110100011", "01... | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
ry(0.34564216457624486) q[0];
rz(pi/2) q[0];
ry(0.1154060501510695) q[1];
ry(1.4069437800814524) q[2];
ry(1.729011663187391) q[3];
ry(1.5443033125665406) q[4];
ry(-0.2054115197914884) q[5];
ry(1.5611251036706755) q[6];
ry(0.017278467754898455) q[7];
ry(1.25331466305098... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"ZIIZIIIIII",
"IIIZIIIIZI",
"ZIIIIIZIII",
"IIIIIIZIZI",
"ZIIIIIIIIZ",
"IIIIIIIIZZ",
"IIIIIIZIIZ",
"IIIIIIZZII",
"IIZZIIIIII",
"ZIZIIIIIII",
"IIZIIIZIII",
"IIZIIIIZII",
"IIIZIZIIII",
"ZIIIIZIIII",
"IIIIIZZIII",
"IIIIIZIIIZ",
"IIZIIZIIII",
"IZIIIIIIZI",
"IZIIIIZIII",
"IIIZZIIIII"... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0.973551 | [
0.34564216457624486,
0.1154060501510695,
1.4069437800814524,
1.729011663187391,
1.5443033125665406,
-0.2054115197914884,
1.5611251036706755,
0.017278467754898455,
1.253314663050988,
0.5147613500249996,
-1.0183755194153328,
0.3407061169539516,
-0.44567575751385724,
-0.15411458017541307,
-... | {
"n_parameters": 40,
"n_qubits": 10,
"optimal_eigenvalue": -4.5,
"target_ratio": 0.97,
"target_value": -4.365
} | 13 |
ac1f174c7c8aefd4d3fe63daa83b99d5 | connected_components | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 3, "target": 6}, {"source": 4, "target": 5}, {"source": 4, "target":... | {"states": [504, 511], "expectation_value": -9.615701312990927, "params": null, "bitstrings": ["000000111", "000000000"], "total_optimization_steps": 100, "probabilities": [0.09588923371402847, 0.4656420535322759], "optimization_time": 174.93005180358887} | -1.5 * (Z(0) @ Z(1)) + 0.5 * (Z(2) @ Z(1)) + -1.5 * (Z(2) @ Z(0)) + -2.0 * (Z(5) @ Z(3)) + -1.5 * (Z(4) @ Z(3)) + 0.5 * (Z(4) @ Z(5)) + -1.5 * (Z(6) @ Z(7)) + -1.5 * (Z(8) @ Z(7)) + 0.5 * (Z(8) @ Z(6)) + 0.5 * Z(1) + 0.5 * Z(0) + 0.5 * Z(2) + 1.0 * Z(3) + -1.0 * Z(5) + 0.5 * Z(4) + 0.5 * Z(7) + 0.5 * Z(6) + 0.5 * Z(8) | 1 | 9 | 1 | {"smallest_eigenvalues": [-11.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -10.5, "smallest_bitstrings": ["000000000"], "largest_eigenvalue": 13.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
ry(0.78394604932781) q[0];
h q[1];
ry(-0.0032434023779111705) q[1];
h q[2];
cx q[2], q[0];
ry(-0.78394604932781) q[0];
cx q[2], q[0];
cx q[0], q[1];
ry(0.0032434023779111705) q[1];
cx q[0], q[1];
ry(2.635476633840907) q[0];
ry(1.7640206425411538) q[2];
cx q[0], ... | null | {"node": 3} | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[9] c;\nqubit[9] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\nh q[8];\ncry(1.5708) q[5], q[3];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc... | [
"IIIIIIIZZ",
"IIIIIIZZI",
"IIIIIIZIZ",
"IIIZIZIII",
"IIIIZZIII",
"IIIZZIIII",
"IZZIIIIII",
"ZZIIIIIII",
"ZIZIIIIII",
"IIIIIIIZI",
"IIIIIIIIZ",
"IIIIIIZII",
"IIIIIZIII",
"IIIZIIIII",
"IIIIZIIII",
"IZIIIIIII",
"IIZIIIIII",
"ZIIIIIIII"
] | [
-1.5,
0.5,
-1.5,
-2,
-1.5,
0.5,
-1.5,
-1.5,
0.5,
0.5,
0.5,
0.5,
1,
-1,
0.5,
0.5,
0.5,
0.5
] | 0.934748 | [
0.449206498865341,
1.56789209865562,
1.2315751440251939,
2.0935582032832687,
0.9606136929073632,
-0.006486804755822341,
2.635476633840907,
0.44855704008979325,
1.7249132980744837,
1.6068138992675811,
-0.3051166391100603,
-0.46114860020241605,
2.3983895329462612,
-1.5814129982760357,
1.05... | {
"n_parameters": 49,
"n_qubits": 9,
"optimal_eigenvalue": -11.5,
"target_ratio": 0.97,
"target_value": -11.155
} | 500 |
04943d12be9331cc9245456617bb8845 | max_flow | adaptive_vqe | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"capacity": 1, "source": 0, "target": 3}, {"capacity": 3, "source": 0, "target": 5}, {"capacity": 1, "source": 1, "target": 4}, {"capacity": 3, "source": 3, "target": 2}, {"capaci... | {"states": [476, 958], "expectation_value": -24.02738615215402, "params": null, "bitstrings": ["1111000100011", "1110001000001"], "total_optimization_steps": 100, "probabilities": [0.15696165053451847, 0.42690998683539116], "optimization_time": 442.1918320655823} | -1.0 * (Z(10) @ Z(3)) + -2.0 * (Z(11) @ Z(3)) + 2.0 * (Z(11) @ Z(10)) + 2.0 * (Z(4) @ Z(5)) + -1.0 * (Z(0) @ Z(5)) + -0.5 * (Z(0) @ Z(4)) + 0.5 * (Z(6) @ Z(3)) + -0.5 * (Z(6) @ Z(10)) + -1.0 * (Z(6) @ Z(11)) + 1.0 * (Z(6) @ Z(5)) + 0.5 * (Z(6) @ Z(4)) + -0.5 * (Z(6) @ Z(0)) + 1.0 * (Z(7) @ Z(3)) + -1.0 * (Z(7) @ Z(10))... | 1 | 13 | 1 | {"smallest_eigenvalues": [-30.5, -30.5, -30.5, -30.5], "number_of_smallest_eigenvalues": 4, "first_excited_energy": -30.25, "smallest_bitstrings": ["1111000010100", "1110000010000", "1111001000101", "1110001000001"], "largest_eigenvalue": 79.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[13] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
ry(2.756448642387936) q[4];
rz(-pi) q[5];
ry(-1.4071951647766399) q[5];
h q[6];
ry(1.5747373492012693) q[6];
cx q[6], q[5];
ry(0.47977392536284186) q[5];
cx q[6], q[5];
ry(-0.018776860890256552) q[5];
cx q[0], q[5];
ry(0.01877686... | null | {"source": 0, "sink": 5} | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[13] c;\nqubit[13] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\nh q[8];\nh q[9];\nh q[10];\nh q[11];\nh q[12];\nry(-2.4156) q[5];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = mea... | [
"IIZIIIIIIZIII",
"IZIIIIIIIZIII",
"IZZIIIIIIIIII",
"IIIIIIIZZIIII",
"IIIIIIIZIIIIZ",
"IIIIIIIIZIIIZ",
"IIIIIIZIIZIII",
"IIZIIIZIIIIII",
"IZIIIIZIIIIII",
"IIIIIIZZIIIII",
"IIIIIIZIZIIII",
"IIIIIIZIIIIIZ",
"IIIIIZIIIZIII",
"IIZIIZIIIIIII",
"IZIIIZIIIIIII",
"IIIIIZIZIIIII",
"IIIIIZIIZII... | [
-1,
-2,
2,
2,
-1,
-0.5,
0.5,
-0.5,
-1,
1,
0.5,
-0.5,
1,
-1,
-2,
2,
1,
-1,
2,
1,
0.5,
-0.5,
0.5,
1,
2,
1,
-1,
1,
2,
1,
-0.5,
0.5,
1,
-0.5,
-1,
-0.25,
-1,
1,
2,
11,
5.5,
-4.125,
4,
8,
4,
8,
0,
-0.75,
-0.375
] | 0.971122 | [
-2.4982175662086945,
-1.2959791973212518,
10.693477959740283,
2.756448642387936,
1.5747373492012693,
-0.9595478507256837,
-0.037553721780513104,
-0.09233073908691143,
0.3924196282534974,
0.01592015931431091,
0.17530178727681012,
-0.09689234899048765,
0.07372477176280937,
0.0220347731740424... | {
"n_parameters": 84,
"n_qubits": 13,
"optimal_eigenvalue": -30.5,
"target_ratio": 0.97,
"target_value": -29.585
} | 96 |
6906407679808988270 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], "hyperedges": [[2, 6], [0, 8], [0, 2], [1, 2], [1, 7], [2, 5], [1, 6], [0, 4], [8, 1], [1, 3], [9, 4]]} | {"states": [254, 238], "expectation_value": -3.9291428938769224, "params": [-0.0066, 0.0004, -0.0074, 0.0006000000000000001, 1.3336000000000001, 1.3607, 1.5598, 1.5534000000000001, 1.4224, 1.659, 0.8604, 0.6572, 1.5783, 1.5912000000000002, 1.4727000000000001, 1.5324, 1.5405, 1.5993000000000002, 0.1797, -0.155, 0.0162, ... | 0.5 * (Z(2) @ Z(6)) + 0.5 * (Z(0) @ Z(2)) + 0.5 * (Z(8) @ Z(0)) + 0.5 * (Z(1) @ Z(6)) + 0.5 * (Z(1) @ Z(2)) + 0.5 * (Z(1) @ Z(8)) + 0.5 * (Z(7) @ Z(1)) + 0.5 * (Z(5) @ Z(2)) + 0.5 * (Z(4) @ Z(0)) + 0.5 * (Z(3) @ Z(1)) + 0.5 * (Z(9) @ Z(4)) + 0.0 * Z(6) + 0.0 * Z(2) + 0.0 * Z(0) + 0.0 * Z(8) + 0.0 * Z(1) + 0.0 * Z(7) + ... | 14 | 10 | 1 | {"smallest_eigenvalues": [-4.5, -4.5, -4.5, -4.5], "number_of_smallest_eigenvalues": 4, "first_excited_energy": -3.5, "smallest_bitstrings": ["0011100110", "1100011001", "1100010001", "0011101110"], "largest_eigenvalue": 5.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
ry(-0.0406105699275701) q[0];
rz(pi/2) q[0];
ry(0.10567355003241799) q[1];
ry(1.6191416972240655) q[2];
ry(1.4849743419172128) q[3];
ry(1.391072321318301) q[4];
ry(0.3277942915188528) q[5];
ry(1.477514880333615) q[6];
ry(1.2748923680720525) q[7];
ry(1.4789354162386323)... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIZIIIZII",
"IIIIIIIZIZ",
"IZIIIIIIIZ",
"IIIZIIIIZI",
"IIIIIIIZZI",
"IZIIIIIIZI",
"IIZIIIIIZI",
"IIIIZIIZII",
"IIIIIZIIIZ",
"IIIIIIZIZI",
"ZIIIIZIIII",
"IIIZIIIIII",
"IIIIIIIZII",
"IIIIIIIIIZ",
"IZIIIIIIII",
"IIIIIIIIZI",
"IIZIIIIIII",
"IIIIZIIIII",
"IIIIIZIIII",
"IIIIIIZIII"... | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0,
0,
0,
0,
0,
0,
0,
0,
0,
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] | 0.985426 | [
-0.0406105699275701,
0.10567355003241799,
1.6191416972240655,
1.4849743419172128,
1.391072321318301,
0.3277942915188528,
1.477514880333615,
1.2748923680720525,
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0.30300915686489766,
0.03822888763372674,
0.1322613406893181,
0.7868894045325173,
0.5763447402558283,
0.5751... | {
"n_parameters": 40,
"n_qubits": 10,
"optimal_eigenvalue": -4.5,
"target_ratio": 0.97,
"target_value": -4.365
} | 11 |
5599bf10ca71927ac876cacb8b12fa55 | vertex_cover | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 5}, {"source": 1, "target": 3}, {"source": 1, "target": 4}, ... | {"states": [22, 69], "expectation_value": -1.7676389138815616, "params": [[0.0641, 0.0702, 0.0765], [-0.057600000000000005, -0.052000000000000005, -0.059800000000000006]], "bitstrings": ["1101001", "0111010"], "total_optimization_steps": 10, "probabilities": [0.01520711769709883, 0.015828097703021293], "optimization_ti... | 0.5 * (Z(0) @ Z(1)) + 0.5 * (Z(2) @ Z(0)) + 0.5 * (Z(3) @ Z(1)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(5) @ Z(1)) + 0.5 * (Z(5) @ Z(0)) + 0.5 * (Z(5) @ Z(3)) + 0.5 * (Z(4) @ Z(1)) + 0.5 * (Z(4) @ Z(3)) + 0.5 * (Z(6) @ Z(1)) + 0.5 * (Z(6) @ Z(2)) + 0.5 * (Z(6) @ Z(3)) + 0.5 * (Z(6) @ Z(5)) + -2.0 * Z(1) ... | 1 | 7 | 3 | {"smallest_eigenvalues": [-6.5, -6.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -5.5, "smallest_bitstrings": ["1101001", "0111010"], "largest_eigenvalue": 17.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.07415269114269459) q[0];
cx q[1], q[0];
h q[2];
cx q[0], q[2];
rz(0.07415269114269459) q[2];
cx q[0], q[2];
h q[3];
cx q[1], q[3];
rz(0.07415269114269459) q[3];
cx q[1], q[3];
cx q[0], q[3];
rz(0.07415269114269459) q[3];
cx q[0], q[3]... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIZZ",
"IIIIZIZ",
"IIIZIZI",
"IIIZIIZ",
"IIIZZII",
"IZIIIZI",
"IZIIIIZ",
"IZIZIII",
"IIZIIZI",
"IIZZIII",
"ZIIIIZI",
"ZIIIZII",
"ZIIZIII",
"ZZIIIII",
"IIIIIZI",
"IIIIIIZ",
"IIIIZII",
"IIIZIII",
"IZIIIII",
"IIZIIII",
"ZIIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-2,
-1.5,
-1,
-2.5,
-1.5,
-0.5,
-1.5
] | 0.864887 | [
0.07415269114269459,
-1.68604805643772,
-1.8099461218403394,
1.443016048934571,
-1.494512272491701,
1.4645976572003123,
1.0927469485153785,
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-0.827568241380443,
-1.2321072303008926,
-0.5239782363821548,
-2.223436606296981,
0.... | {
"n_parameters": 21,
"n_qubits": 7,
"optimal_eigenvalue": -6.5,
"target_ratio": 0.97,
"target_value": -6.305
} | 500 |
e6db2dfa08ae604c90d51443a84ac3aa | connected_components | adaptive_vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}, {"id": 10}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": ... | {"states": [127, 895], "expectation_value": -16.148276845510008, "params": null, "bitstrings": ["1110000000", "0010000000"], "total_optimization_steps": 100, "probabilities": [0.056403061430086616, 0.525069991821818], "optimization_time": 191.35102701187134} | -2.5 * (Z(0) @ Z(1)) + 0.5 * (Z(3) @ Z(1)) + -2.5 * (Z(3) @ Z(0)) + 0.5 * (Z(4) @ Z(1)) + -2.5 * (Z(4) @ Z(0)) + -2.0 * (Z(4) @ Z(3)) + 0.5 * (Z(5) @ Z(1)) + -2.5 * (Z(5) @ Z(0)) + 1.0 * (Z(5) @ Z(3)) + -2.0 * (Z(5) @ Z(4)) + -2.0 * (Z(6) @ Z(7)) + -1.5 * (Z(8) @ Z(7)) + -2.0 * (Z(8) @ Z(6)) + 0.5 * (Z(9) @ Z(7)) + -2.... | 5 | 10 | 1 | {"smallest_eigenvalues": [-23.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -22.0, "smallest_bitstrings": ["0010000000"], "largest_eigenvalue": 18.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[10] q;
h q[0];
ry(0.32146682918983277) q[0];
h q[1];
h q[2];
h q[3];
ry(0.710109290808981) q[3];
h q[4];
ry(0.32146682918983277) q[4];
h q[5];
cx q[5], q[0];
ry(-0.32146682918983277) q[0];
cx q[5], q[0];
cx q[0], q[4];
ry(-0.32146682918983277) q[4];
cx q[0], q[4];
cx q[4], q[... | null | {"node": 9} | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[10] c;\nqubit[10] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nh q[7];\nh q[8];\nh q[9];\ncry(1.5708) q[5], q[0];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measu... | [
"IIIIIIIIZZ",
"IIIIIIZIZI",
"IIIIIIZIIZ",
"IIIIIZIIZI",
"IIIIIZIIIZ",
"IIIIIZZIII",
"IIIIZIIIZI",
"IIIIZIIIIZ",
"IIIIZIZIII",
"IIIIZZIIII",
"IIZZIIIIII",
"IZZIIIIIII",
"IZIZIIIIII",
"ZIZIIIIIII",
"ZIIZIIIIII",
"ZZIIIIIIII",
"IIIIIIIIZI",
"IIIIIIIIIZ",
"IIIIIIZIII",
"IIIIIZIIII"... | [
-2.5,
0.5,
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0.5,
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1,
-2,
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-2,
0.5,
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0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
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] | 0.962909 | [
0.6429336583796655,
1.420218581617962,
0.7301720949807214,
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0.5352653895369367,
0.973064560113228,
0.032924739863521554,
0.040913603743331924,
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1.3563168142516644,
0.19031197915580272,
-0.017749471946519643,
0.10632444600795163,
-0.3087380877661796,
... | {
"n_parameters": 74,
"n_qubits": 10,
"optimal_eigenvalue": -23,
"target_ratio": 0.97,
"target_value": -22.31
} | 500 |
60c88ab22b149e82bb7da24a7941f270 | vertex_cover | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 1, "target": 2}, {"source": 1, "target": 6}, {"source": 2, "target": 4}, ... | {"states": [70, 38], "expectation_value": -0.3768810581325747, "params": [[-0.07740000000000001], [0.07590000000000001]], "bitstrings": ["0111001", "1011001"], "total_optimization_steps": 10, "probabilities": [0.009430395502179419, 0.00943039550217942], "optimization_time": 1.642801284790039} | 0.5 * (Z(0) @ Z(1)) + 0.5 * (Z(2) @ Z(1)) + 0.5 * (Z(2) @ Z(0)) + 0.5 * (Z(3) @ Z(0)) + 0.5 * (Z(6) @ Z(1)) + 0.5 * (Z(6) @ Z(3)) + 0.5 * (Z(4) @ Z(2)) + 0.5 * (Z(4) @ Z(3)) + 0.5 * (Z(4) @ Z(6)) + 0.5 * (Z(5) @ Z(2)) + 0.5 * (Z(5) @ Z(3)) + 0.5 * (Z(5) @ Z(6)) + -1.0 * Z(1) + -1.0 * Z(0) + -1.5 * Z(2) + -1.5 * Z(3) + ... | 1 | 7 | 1 | {"smallest_eigenvalues": [-5.5, -5.5], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -4.5, "smallest_bitstrings": ["0111001", "1011001"], "largest_eigenvalue": 14.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(1.33887067804164e-08) q[0];
cx q[1], q[0];
h q[2];
cx q[1], q[2];
rz(1.33887067804164e-08) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(1.33887067804164e-08) q[2];
cx q[0], q[2];
h q[3];
cx q[0], q[3];
rz(1.33887067804164e-08) q[3];
cx q[0], ... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
bit[7] c;
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[1], q[0];
rz(x0) q[0];
cx q[1], q[0];
cx q[1], q[2];
rz(x0) q[2];
cx q[1], q[2];
cx q[0], q[2];
rz(x0) q[2];
cx q[0], q... | null | {"circuits": [], "gradients": []} | [
"IIIIIZZ",
"IIIIZZI",
"IIIIZIZ",
"IIIZIIZ",
"ZIIIIZI",
"ZIIZIII",
"IIZIZII",
"IIZZIII",
"ZIZIIII",
"IZIIZII",
"IZIZIII",
"ZZIIIII",
"IIIIIZI",
"IIIIIIZ",
"IIIIZII",
"IIIZIII",
"ZIIIIII",
"IIZIIII",
"IZIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1,
-1,
-1.5,
-1.5,
-1.5,
-1,
-1
] | 0.818182 | [
1.33887067804164e-8,
-1.570180603237012,
1.5707963324338174,
1.570796291382669
] | {
"n_parameters": 4,
"n_qubits": 7,
"optimal_eigenvalue": -5.5,
"target_ratio": 0.97,
"target_value": -5.335
} | 155 |
b80d831cd9b07b1f2aaf1d64249cf046 | edge_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}], "edges": [{"source": 0, "target": 1}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 1, "target": 5}, {"source": 1, "target": 6}, {"source": 2, "target": 3}, ... | {"states": [42, 106], "expectation_value": -1.6396914489961478, "params": [0.0025, 0.5702, 0.7993, 0.0041, 0.8, 0.0002, 0.0024000000000000002, 0.5995, 0.8091, 0.007, 0.5651, 0.21450000000000002, 0.7979, 0.23450000000000001, 0.30210000000000004, 0.48500000000000004, 0.0025, 0.0063, 0.7972, 0.0053, 0.7977000000000001, 0.... | 0.0625 * (Z(0) @ Z(1)) + 0.0625 * (Z(0) @ Z(2)) + 0.0625 * (Z(0) @ Z(3)) + 0.0625 * (Z(0) @ Z(4)) + 0.0625 * (Z(1) @ Z(2)) + 0.0625 * (Z(1) @ Z(3)) + 0.0625 * (Z(4) @ Z(1)) + 0.0625 * (Z(2) @ Z(3)) + 0.0625 * (Z(4) @ Z(2)) + 0.0625 * (Z(4) @ Z(3)) + -0.0625 * (Z(0) @ Z(1) @ Z(2)) + -0.0625 * (Z(0) @ Z(1) @ Z(3)) + -0.0... | 16 | 8 | 2 | {"smallest_eigenvalues": [-3.8125], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.8125, "smallest_bitstrings": ["10010101"], "largest_eigenvalue": 6.1875} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rx(0.057187703765313375) q[0];
rz(0.7690216135978227) q[0];
rx(1.209906049124608) q[1];
rz(-0.07290860364248924) q[1];
cx q[1], q[0];
rz(-0.028593851882656687) q[0];
cx q[1], q[0];
rx(0.05718770376531337) q[0];
rz(-0.6005090386584673) q[0];
rz(0.11078862637344898) q[1];... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIZZ",
"IIIIIZIZ",
"IIIIZIIZ",
"IIIZIIIZ",
"IIIIIZZI",
"IIIIZIZI",
"IIIZIIZI",
"IIIIZZII",
"IIIZIZII",
"IIIZZIII",
"IIIIIZZZ",
"IIIIZIZZ",
"IIIZIIZZ",
"IIIIZZIZ",
"IIIZIZIZ",
"IIIZZIIZ",
"IIIIZZZI",
"IIIZIZZI",
"IIIZZIZI",
"IIIZZZII",
"IIIIZZZZ",
"IIIZIZZZ",
"IIIZZIZ... | [
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
0.25,
0.25,
0.25,
-0.25,
0.5,
0.5,
... | 0.97207 | [
0.057187703765313375,
0.7404277617151661,
1.209906049124608,
-0.07290860364248924,
1.2903415687138335,
-0.07675919091913075,
0.10497633905354888,
-0.06733609960099873,
1.3402996070483726,
-0.03416843960718164,
0.03206647432155457,
0.5921790357738657,
1.793709390858471,
0.1755954028706419,
... | {
"n_parameters": 42,
"n_qubits": 8,
"optimal_eigenvalue": -3.8125,
"target_ratio": 0.97,
"target_value": -3.698125
} | 21 |
d6a0416211a923ad5745888e36470119 | connected_components | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}, {"id": 9}], "edges": [{"source": 0, "target": 2}, {"source": 0, "target": 5}, {"source": 1, "target": 2}, {"source": 1, "target": 3}, {"source": 1, "target":... | {"states": [504, 511], "expectation_value": -0.09663924400753071, "params": [[-0.0158], [0.0155]], "bitstrings": ["000000111", "000000000"], "total_optimization_steps": 10, "probabilities": [0.0020254127781950382, 0.002027387994519636], "optimization_time": 2.0815999507904053} | -2.0 * (Z(0) @ Z(2)) + 0.5 * (Z(5) @ Z(2)) + -2.0 * (Z(5) @ Z(0)) + -2.5 * (Z(1) @ Z(2)) + 0.5 * (Z(1) @ Z(0)) + 0.5 * (Z(1) @ Z(5)) + 0.5 * (Z(3) @ Z(2)) + 0.5 * (Z(3) @ Z(0)) + -2.5 * (Z(3) @ Z(5)) + -2.5 * (Z(3) @ Z(1)) + 0.5 * (Z(4) @ Z(2)) + 0.5 * (Z(4) @ Z(5)) + -2.0 * (Z(4) @ Z(1)) + -2.0 * (Z(4) @ Z(3)) + -2.0 ... | 5 | 9 | 1 | {"smallest_eigenvalues": [-21.0], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -20.0, "smallest_bitstrings": ["000000000"], "largest_eigenvalue": 18.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
h q[0];
h q[1];
h q[2];
cx q[2], q[0];
rz(0.9569136646013533) q[0];
cx q[2], q[0];
h q[3];
h q[4];
h q[5];
cx q[2], q[5];
rz(0.1844350780294243) q[5];
cx q[2], q[5];
cx q[0], q[5];
cx q[2], q[1];
rz(0.5813071740482846) q[1];
cx q[2], q[1];
cx q[2], q[3];
rz(0.1844350780... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
bit[9] c;
qubit[9] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
h q[7];
h q[8];
cx q[2], q[0];
rz(x0) q[0];
cx q[2], q[0];
cx q[2], q[5];
rz(x1) q[5... | {"node": 7} | {"circuits": [], "gradients": []} | [
"IIIIIIZIZ",
"IIIZIIZII",
"IIIZIIIIZ",
"IIIIIIZZI",
"IIIIIIIZZ",
"IIIZIIIZI",
"IIIIIZZII",
"IIIIIZIIZ",
"IIIZIZIII",
"IIIIIZIZI",
"IIIIZIZII",
"IIIZZIIII",
"IIIIZIIZI",
"IIIIZZIII",
"IZZIIIIII",
"ZZIIIIIII",
"ZIZIIIIII",
"IIIIIIZII",
"IIIIIIIIZ",
"IIIZIIIII",
"IIIIIIIZI",
"... | [
-2,
0.5,
-2,
-2.5,
0.5,
0.5,
0.5,
0.5,
-2.5,
-2.5,
0.5,
0.5,
-2,
-2,
-2,
-1.5,
-2,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
1,
-1.5,
1
] | 0.584934 | [
0.9569136646013533,
0.1844350780294243,
0.5813071740482846,
0.6654976616408042,
0.0035534887737996546,
0.9669021796980994
] | {
"n_parameters": 6,
"n_qubits": 9,
"optimal_eigenvalue": -21,
"target_ratio": 0.97,
"target_value": -20.37
} | 159 |
90ed954541db23a75eecb07977c28089 | edge_cover | qaoa | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"source": 0, "target": 1}, {"source": 0, "target": 2}, {"source": 0, "target": 3}, {"source": 0, "target": 4}, {"source": 0, "target": 5}, {"source": 1, "target": 4}, {"source": ... | {"states": [3791, 3887], "expectation_value": -0.40364448955729515, "params": [[-0.0835, -0.0777, -0.0746], [0.0795, 0.07390000000000001, 0.0693]], "bitstrings": ["000100110000", "000011010000"], "total_optimization_steps": 10, "probabilities": [0.0005677207525938194, 0.0005677207525938201], "optimization_time": 36.925... | 0.0625 * (Z(0) @ Z(1)) + 0.0625 * (Z(0) @ Z(2)) + 0.0625 * (Z(0) @ Z(3)) + 0.0625 * (Z(0) @ Z(4)) + 0.0625 * (Z(1) @ Z(2)) + 0.0625 * (Z(1) @ Z(3)) + 0.0625 * (Z(1) @ Z(4)) + 0.0625 * (Z(2) @ Z(3)) + 0.0625 * (Z(2) @ Z(4)) + 0.0625 * (Z(3) @ Z(4)) + -0.0625 * (Z(0) @ Z(1) @ Z(2)) + -0.0625 * (Z(0) @ Z(1) @ Z(3)) + -0.0... | 1 | 12 | 3 | {"smallest_eigenvalues": [-3.8125, -3.8125, -3.8125, -3.8125, -3.8125, -3.8125, -3.8125, -3.8125], "number_of_smallest_eigenvalues": 8, "first_excited_energy": -2.8125, "smallest_bitstrings": ["010001000001", "000011010000", "100000000110", "001000101000", "100000001001", "000100110000", "001001000100", "010000100010"]... | OPENQASM 3.0;
include "stdgates.inc";
qubit[12] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.3009393722060807) q[0];
cx q[1], q[0];
h q[2];
cx q[2], q[0];
rz(0.3009393722060807) q[0];
cx q[2], q[0];
cx q[2], q[1];
rz(0.3009393722060807) q[1];
cx q[2], q[1];
h q[3];
cx q[3], q[0];
rz(0.3009393722060807) q[0];
cx q[3], q[0];
c... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIIIIIIIIIZZ",
"IIIIIIIIIZIZ",
"IIIIIIIIZIIZ",
"IIIIIIIZIIIZ",
"IIIIIIIIIZZI",
"IIIIIIIIZIZI",
"IIIIIIIZIIZI",
"IIIIIIIIZZII",
"IIIIIIIZIZII",
"IIIIIIIZZIII",
"IIIIIIIIIZZZ",
"IIIIIIIIZIZZ",
"IIIIIIIZIIZZ",
"IIIIIIIIZZIZ",
"IIIIIIIZIZIZ",
"IIIIIIIZZIIZ",
"IIIIIIIIZZZI",
"IIIIIIIZI... | [
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
-0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
0.0625,
-0.0625,
0.25,
0.25,
0.25,
-0.25,
0.125,
0.1... | 0.807446 | [
0.3009393722060807,
1.2484013044131173,
-0.3798378390662217,
0.4270385845264586,
-0.18410433411884003,
0.15621560101591658,
0.7528483255570873,
0.46142641491757197,
0.9481662270374182,
-0.565569105340614,
-0.3443169043342043,
-0.45828684618528925,
0.6868535447971575,
-0.27349808895761746,
... | {
"n_parameters": 27,
"n_qubits": 12,
"optimal_eigenvalue": -3.8125,
"target_ratio": 0.97,
"target_value": -3.698125
} | 500 |
6ba19468e6c5e5082f99c29552d3272c | matching | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"bipartite": 0, "id": 0}, {"bipartite": 0, "id": 1}, {"bipartite": 0, "id": 2}, {"bipartite": 0, "id": 3}, {"bipartite": 0, "id": 4}, {"bipartite": 0, "id": 5}, {"bipartite": 0, "id": 6}, {"bipartite": 0, "id": 7}, {"bipartite": 0, "id": 8}, {"bipartite":... | {"states": [1482, 1226], "expectation_value": -121.6074651891478, "params": [[[0.5222, 0.0034000000000000002], [0.021, -0.0035], [0.7653000000000001, 0.0066], [0.7521, 0.0047], [1.5777, 0.5674], [-0.0055000000000000005, 0.6129], [0.012400000000000001, 0.2696], [0.1738, 1.4587], [0.006500000000000001, 1.5858], [1.4107, ... | 8.0 * (Z(1) @ Z(0)) + 8.0 * (Z(3) @ Z(2)) + 8.0 * (Z(4) @ Z(2)) + 8.0 * (Z(5) @ Z(0)) + 8.0 * (Z(5) @ Z(4)) + 8.0 * (Z(6) @ Z(3)) + 8.0 * (Z(7) @ Z(2)) + 8.0 * (Z(7) @ Z(4)) + 8.0 * (Z(8) @ Z(7)) + 8.0 * (Z(9) @ Z(2)) + 8.0 * (Z(9) @ Z(4)) + 8.0 * (Z(9) @ Z(7)) + 8.0 * (Z(10) @ Z(9)) + 7.5 * Z(0) + -6.5 * Z(1) + 20.0 *... | 15 | 11 | 2 | {"smallest_eigenvalues": [-140.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -118.5, "smallest_bitstrings": ["01100110101"], "largest_eigenvalue": 190.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[11] q;
ry(0.59566002304461) q[0];
ry(-0.04627544935789368) q[1];
ry(-0.19835683630421863) q[2];
ry(1.1496475053642552) q[3];
ry(1.6034484102893993) q[4];
ry(-0.03350944038619226) q[5];
ry(-0.11809811984486834) q[6];
ry(0.04000024070580695) q[7];
ry(-0.016866784589919442) q[8]... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | {"matching": "maximum_bipartite", "extra": "{\"left_nodes\": [0, 1, 2, 3, 4, 5, 6, 7, 8], \"right_nodes\": [9, 10, 11, 12, 13, 14]}"} | {"circuits": [], "gradients": []} | [
"IIIIIIIIIZZ",
"IIIIIIIZZII",
"IIIIIIZIZII",
"IIIIIZIIIIZ",
"IIIIIZZIIII",
"IIIIZIIZIII",
"IIIZIIIIZII",
"IIIZIIZIIII",
"IIZZIIIIIII",
"IZIIIIIIZII",
"IZIIIIZIIII",
"IZIZIIIIIII",
"ZZIIIIIIIII",
"IIIIIIIIIIZ",
"IIIIIIIIIZI",
"IIIIIIIIZII",
"IIIIIIIZIII",
"IIIIIIZIIII",
"IIIIIZIII... | [
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
8,
7.5,
-6.5,
20,
5.5,
22,
3.5,
-7.5,
25,
-3,
25.5,
-5.5
] | 0.974101 | [
0.59566002304461,
-0.04627544935789368,
-0.19835683630421863,
1.1496475053642552,
1.6034484102893993,
-0.03350944038619226,
-0.11809811984486834,
0.04000024070580695,
-0.016866784589919442,
1.054978435777813,
1.5993207690557243,
0.029653818988561616,
0.0551534475373922,
0.04781913380972297... | {
"n_parameters": 42,
"n_qubits": 11,
"optimal_eigenvalue": -140.5,
"target_ratio": 0.97,
"target_value": -136.285
} | 32 |
6272802841015324019 | hypermaxcut | qaoa | {"nodes": [0, 1, 2, 3, 4, 5, 6], "hyperedges": [[1, 2, 4], [2, 3, 6], [3, 4, 5], [0, 1]]} | {"states": [58, 45], "expectation_value": -0.00010996751996814047, "params": [[-0.003], [0.0064]], "bitstrings": ["1000101", "1010010"], "total_optimization_steps": 10, "probabilities": [0.007814016205355805, 0.007814016205355807], "optimization_time": 1.6616637706756592} | 0.16666666666666666 * (Z(1) @ Z(2)) + 0.16666666666666666 * (Z(4) @ Z(2)) + 0.16666666666666666 * (Z(4) @ Z(1)) + 0.16666666666666666 * (Z(3) @ Z(2)) + 0.16666666666666666 * (Z(3) @ Z(4)) + 0.16666666666666666 * (Z(6) @ Z(2)) + 0.16666666666666666 * (Z(6) @ Z(3)) + 0.16666666666666666 * (Z(5) @ Z(4)) + 0.16666666666666... | 1 | 7 | 1 | {"smallest_eigenvalues": [-1.5, -1.5, -1.5], "number_of_smallest_eigenvalues": 3, "first_excited_energy": -1.4999999999999996, "smallest_bitstrings": ["0101000", "1010010", "1000101"], "largest_eigenvalue": 3.499999999999999} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
h q[1];
h q[2];
cx q[2], q[1];
rz(-0.2881550897283588) q[1];
cx q[2], q[1];
h q[3];
h q[4];
cx q[2], q[4];
rz(-0.2881550897283588) q[4];
cx q[2], q[4];
cx q[1], q[4];
cx q[2], q[3];
rz(-0.2881550897283588) q[3];
cx q[2], q[3];
rz(-0.2881550897283588) q[4];
cx q[... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x2;
input float[64] x3;
input float[64] x4;
bit[7] c;
qubit[7] q;
h q[0];
h q[1];
h q[2];
h q[3];
h q[4];
h q[5];
h q[6];
cx q[2], q[1];
rz(x0) q[1];
cx q[2], q[1];
cx q[2], q[4];
rz(x0) q[4];
cx q[2], q[4];
cx q[1], q[4];
rz(... | null | {"circuits": [], "gradients": []} | [
"IIIIZZI",
"IIZIZII",
"IIZIIZI",
"IIIZZII",
"IIZZIII",
"ZIIIZII",
"ZIIZIII",
"IZZIIII",
"IZIZIII",
"IIIIIZZ",
"IIIIZII",
"IIIIIZI",
"IIZIIII",
"IIIZIII",
"ZIIIIII",
"IZIIIII",
"IIIIIIZ"
] | [
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.5,
0.3333333333333333,
0.16666666666666663,
0.3333333333333333,
0.3333333333333333,
0.16666666666... | 0.696588 | [
-0.2881550897283588,
-1.496924056958604,
-0.8702342626006511,
0.27763552226674554,
0.8275140809017422
] | {
"n_parameters": 5,
"n_qubits": 7,
"optimal_eigenvalue": -1.5,
"target_ratio": 0.97,
"target_value": -1.455
} | 131 |
-2070272192972975425 | hypermaxcut | adaptive_vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6], "hyperedges": [[0, 1, 2, 4, 6], [2, 3, 4, 5], [0, 1, 5, 6], [1, 3, 4, 5, 6], [0, 2, 4, 5, 6], [1, 2, 3], [0, 3, 6], [0, 1, 4, 5], [1, 2, 4, 5], [0, 3, 4]]} | {"states": [103, 47], "expectation_value": -2.350605613821749, "params": null, "bitstrings": ["0011000", "1010000"], "total_optimization_steps": 34, "probabilities": [0.043873417488404634, 0.9020331826068068], "optimization_time": 46.748924255371094} | 0.21666666666666667 * (Z(0) @ Z(1)) + 0.3 * (Z(2) @ Z(1)) + 0.1 * (Z(2) @ Z(0)) + 0.26666666666666666 * (Z(4) @ Z(1)) + 0.35 * (Z(4) @ Z(0)) + 0.26666666666666666 * (Z(4) @ Z(2)) + 0.18333333333333335 * (Z(6) @ Z(1)) + 0.35 * (Z(6) @ Z(0)) + 0.1 * (Z(6) @ Z(2)) + 0.15000000000000002 * (Z(6) @ Z(4)) + 0.2166666666666666... | 1 | 7 | 1 | {"smallest_eigenvalues": [-2.3999999999999995], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -2.3166666666666664, "smallest_bitstrings": ["1010000"], "largest_eigenvalue": 10.000000000000004} | OPENQASM 3.0;
include "stdgates.inc";
qubit[7] q;
h q[0];
ry(-0.3625046353733305) q[0];
h q[1];
ry(1.503895517678477) q[1];
h q[2];
ry(-0.3867772164845615) q[2];
h q[3];
cx q[3], q[0];
ry(0.3625046353733305) q[0];
cx q[3], q[0];
ry(-0.28342853089207637) q[0];
cx q[1], q[0];
ry(0.28342853089207637) q[0];
cx q[1], q[0];
... | null | null | {"circuits": ["OPENQASM 3.0;\ninclude \"stdgates.inc\";\nbit[7] c;\nqubit[7] q;\nh q[0];\nh q[1];\nh q[2];\nh q[3];\nh q[4];\nh q[5];\nh q[6];\nry(1.56) q[4];\nc[0] = measure q[0];\nc[1] = measure q[1];\nc[2] = measure q[2];\nc[3] = measure q[3];\nc[4] = measure q[4];\nc[5] = measure q[5];\nc[6] = measure q[6];\n", "OP... | [
"IIIIIZZ",
"IIIIZZI",
"IIIIZIZ",
"IIZIIZI",
"IIZIIIZ",
"IIZIZII",
"ZIIIIZI",
"ZIIIIIZ",
"ZIIIZII",
"ZIZIIII",
"IIIZIZI",
"IIIZIIZ",
"IIIZZII",
"IIZZIII",
"ZIIZIII",
"IZIIIZI",
"IZIIIIZ",
"IZIIZII",
"IZZIIII",
"ZZIIIII",
"IZIZIII",
"IIIIIZI",
"IIIIIIZ",
"IIIIZII",
"IIZ... | [
0.21666666666666667,
0.3,
0.1,
0.26666666666666666,
0.35,
0.26666666666666666,
0.18333333333333335,
0.35,
0.1,
0.15000000000000002,
0.21666666666666667,
0.3333333333333333,
0.25,
0.3,
0.21666666666666667,
0.3,
0.21666666666666667,
0.21666666666666667,
0.35,
0.18333333333333335,... | 0.976639 | [
1.707721765765945,
1.503895517678477,
1.0256034988578786,
-0.725009270746661,
0.43054185753595337,
0.2032529586797146,
-0.5668570617841527,
0.541345575213752,
-0.773554432969123,
-0.590307615390818,
0.512043244646059,
-0.3919257894255204,
0.37851236353647283,
-0.44905473006266283,
0.3330... | {
"n_parameters": 30,
"n_qubits": 7,
"optimal_eigenvalue": -2.3999999999999995,
"target_ratio": 0.97,
"target_value": -2.3279999999999994
} | 1 |
ac36c5a153720f2afd43ce774542e80a | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"capacity": 1, "source": 0, "target": 1}, {"capacity": 6, "source": 0, "target": 3}, {"capacity": 3, "source": 1, "target": 3}, {"capacity": 3, "source": 1, "target": 4}, {"capaci... | {"states": [32, 31], "expectation_value": -0.08670274291519937, "params": [[0.0159], [-0.0257]], "bitstrings": ["011111", "100000"], "total_optimization_steps": 10, "probabilities": [0.0161088752912674, 0.016133549603724626], "optimization_time": 1.730738878250122} | -0.25 * (Z(0) @ Z(1)) + -2.25 * (Z(3) @ Z(1)) + -1.5 * (Z(3) @ Z(0)) + -2.5 * (Z(4) @ Z(1)) + -0.75 * (Z(4) @ Z(3)) + -1.5 * (Z(5) @ Z(1)) + 2.0 * (Z(5) @ Z(0)) + -1.0 * (Z(5) @ Z(4)) + -0.75 * (Z(2) @ Z(3)) + -0.75 * (Z(2) @ Z(4)) + -0.5 * Z(1) + -0.25 * Z(0) + -1.25 * Z(3) + 2.5 * Z(4) + -0.5 * Z(5) + 0.0 * Z(2) | 1 | 6 | 1 | {"smallest_eigenvalues": [-10.25], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -9.25, "smallest_bitstrings": ["100000"], "largest_eigenvalue": 10.75} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(0.05068074801498348) q[0];
cx q[1], q[0];
h q[2];
h q[3];
cx q[1], q[3];
rz(-0.9068776481257712) q[3];
cx q[1], q[3];
cx q[0], q[3];
rz(-0.21807639072518945) q[3];
cx q[0], q[3];
h q[4];
cx q[1], q[4];
rz(-0.8389376578690388) q[4];
cx q... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64] x6;
input float[64] x7;
input float[64] x8;
input float[64] x9;
bit[6] c;
qubit[6] q;
h q[0];
h q[1];
h ... | {"source": 0, "sink": 5} | {"circuits": [], "gradients": []} | [
"IIIIZZ",
"IIZIZI",
"IIZIIZ",
"IZIIZI",
"IZZIII",
"ZIIIZI",
"ZIIIIZ",
"ZZIIII",
"IIZZII",
"IZIZII",
"IIIIZI",
"IIIIIZ",
"IIZIII",
"IZIIII",
"ZIIIII",
"IIIZII"
] | [
-0.25,
-2.25,
-1.5,
-2.5,
-0.75,
-1.5,
2,
-1,
-0.75,
-0.75,
-0.5,
-0.25,
-1.25,
2.5,
-0.5,
0
] | 0.672188 | [
0.05068074801498348,
-0.9068776481257712,
-0.21807639072518945,
-0.8389376578690388,
-0.5234317396873804,
1.2952058031180758,
-0.19869109614486527,
-0.03125778857127778,
-0.20889072827163999,
0.4804048469203415,
0.13591911593430336,
-0.9021481901189203
] | {
"n_parameters": 12,
"n_qubits": 6,
"optimal_eigenvalue": -10.25,
"target_ratio": 0.97,
"target_value": -9.942499999999999
} | 256 |
7612844348063935763 | hypermaxcut | vqe | {"nodes": [0, 1, 2, 3, 4, 5, 6, 7], "hyperedges": [[0, 5, 6], [0, 2, 4], [3, 5, 7], [0, 1], [5, 6, 7], [1, 6]]} | {"states": [147, 155], "expectation_value": -1.1947223261077125, "params": [1.0018, 0.0016, 0.9873000000000001, 0.0032, 0.9843000000000001, 0.0045000000000000005, 0.3803, 0.007, 0.9999, -0.0011, 0.9982000000000001, 0.0071, 1.0031, 0.0041, 0.9984000000000001, 0.0041, 1.0077, 0.0018000000000000002, 0.9949, 0.0033, 1.0017... | 0.16666666666666666 * (Z(0) @ Z(5)) + 0.3333333333333333 * (Z(6) @ Z(5)) + 0.16666666666666666 * (Z(6) @ Z(0)) + 0.16666666666666666 * (Z(2) @ Z(0)) + 0.16666666666666666 * (Z(4) @ Z(0)) + 0.16666666666666666 * (Z(4) @ Z(2)) + 0.16666666666666666 * (Z(3) @ Z(5)) + 0.3333333333333333 * (Z(7) @ Z(5)) + 0.1666666666666666... | 6 | 8 | 1 | {"smallest_eigenvalues": [-2.3333333333333335, -2.3333333333333335], "number_of_smallest_eigenvalues": 2, "first_excited_energy": -2.0, "smallest_bitstrings": ["01001100", "01100100"], "largest_eigenvalue": 5.0} | OPENQASM 3.0;
include "stdgates.inc";
qubit[8] q;
rx(2.516207018377933) q[0];
rz(1.4660120365496745) q[0];
rx(0.28719118371870084) q[1];
rz(1.3205302404175043) q[1];
rx(2.6788664275891296) q[2];
rz(1.2933296945770225) q[2];
rx(1.7624826631143962) q[3];
rz(1.4726535758948103) q[3];
rx(1.706486446093841) q[4];
rz(1.64122... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x17;
input float[64] x18;
input float[64] x19;
input float[64] x2;
input float[... | null | {"circuits": [], "gradients": []} | [
"IIZIIIIZ",
"IZZIIIII",
"IZIIIIIZ",
"IIIIIZIZ",
"IIIZIIIZ",
"IIIZIZII",
"IIZIZIII",
"ZIZIIIII",
"ZZIIIIII",
"ZIIIZIII",
"IIIIIIZZ",
"IZIIIIZI",
"IIZIIIII",
"IIIIIIIZ",
"IZIIIIII",
"IIIIIZII",
"IIIZIIII",
"IIIIZIII",
"ZIIIIIII",
"IIIIIIZI"
] | [
0.16666666666666666,
0.3333333333333333,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.16666666666666666,
0.3333333333333333,
0.16666666666666666,
0.16666666666666666,
0.5,
0.5,
0.5,
0.33333333333333326,
0.33333333333333326,
0.16666666666666666,
... | 0.970667 | [
2.516207018377933,
-0.10478429024522179,
0.2871911837187009,
-0.2502660863773923,
2.6788664275891296,
-0.27746663221787393,
1.7624826631143966,
-0.09814275090008617,
1.706486446093841,
0.07042732107738664,
2.641537997379765,
0.1645749837916984,
2.7121513947066362,
-0.013779540884130317,
... | {
"n_parameters": 38,
"n_qubits": 8,
"optimal_eigenvalue": -2.3333333333333335,
"target_ratio": 0.97,
"target_value": -2.263333333333333
} | 148 |
43307769d8a05a2ca68cecbc0fed0778 | min_cut | qaoa | {"directed": true, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}], "edges": [{"capacity": 1, "source": 0, "target": 1}, {"capacity": 1, "source": 0, "target": 4}, {"capacity": 2, "source": 1, "target": 5}, {"capacity": 1, "source": 2, "target": 1}, {"capaci... | {"states": [25, 31], "expectation_value": -0.2752042334109547, "params": [[0.060000000000000005, 0.0752], [-0.0398, -0.0682]], "bitstrings": ["100110", "100000"], "total_optimization_steps": 10, "probabilities": [0.019414950188358107, 0.020064667507628517], "optimization_time": 2.7074880599975586} | -0.25 * (Z(0) @ Z(1)) + -0.25 * (Z(4) @ Z(0)) + -0.5 * (Z(5) @ Z(1)) + 0.75 * (Z(5) @ Z(0)) + -0.25 * (Z(2) @ Z(1)) + -0.5 * (Z(2) @ Z(4)) + -0.25 * (Z(2) @ Z(5)) + -0.75 * (Z(3) @ Z(4)) + -0.25 * (Z(3) @ Z(5)) + 0.0 * Z(1) + -0.25 * Z(0) + -1.0 * Z(4) + -0.25 * Z(5) + 1.0 * Z(2) + 0.5 * Z(3) | 1 | 6 | 2 | {"smallest_eigenvalues": [-3.25, -3.25, -3.25], "number_of_smallest_eigenvalues": 3, "first_excited_energy": -2.25, "smallest_bitstrings": ["100000", "100110", "100010"], "largest_eigenvalue": 5.75} | OPENQASM 3.0;
include "stdgates.inc";
qubit[6] q;
h q[0];
h q[1];
cx q[1], q[0];
rz(-0.00023124809840155782) q[0];
cx q[1], q[0];
h q[2];
h q[3];
h q[4];
cx q[0], q[4];
rz(-0.00023124809840155782) q[4];
cx q[0], q[4];
h q[5];
cx q[1], q[5];
rz(0.00030875566784865986) q[5];
cx q[1], q[5];
cx q[0], q[5];
cx q[1], q[2];
r... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x11;
input float[64] x12;
input float[64] x13;
input float[64] x14;
input float[64] x15;
input float[64] x16;
input float[64] x2;
input float[64] x3;
input float[64] x4;
input float[64] x5;
input float[64]... | {"source": 0, "sink": 5} | {"circuits": [], "gradients": []} | [
"IIIIZZ",
"IZIIIZ",
"ZIIIZI",
"ZIIIIZ",
"IIIZZI",
"IZIZII",
"ZIIZII",
"IZZIII",
"ZIZIII",
"IIIIZI",
"IIIIIZ",
"IZIIII",
"ZIIIII",
"IIIZII",
"IIZIII"
] | [
-0.25,
-0.25,
-0.5,
0.75,
-0.25,
-0.5,
-0.25,
-0.75,
-0.25,
0,
-0.25,
-1,
-0.25,
1,
0.5
] | 0.846154 | [
-0.00023124809840155782,
0.00030875566784865986,
2.3115568584055075,
-3.216564759806828,
0.829794500941834,
-0.06741882085370919,
0.8321285704967755,
-0.06948214412449785,
0.5773648280487796,
0.00021406035029157414,
-0.0003257371873867132,
1.986953820724666,
-1.4634239239165174,
-1.0938387... | {
"n_parameters": 17,
"n_qubits": 6,
"optimal_eigenvalue": -3.25,
"target_ratio": 0.97,
"target_value": -3.1525
} | 500 |
48b5e88333d563de0343d06f94299301 | vertex_cover | vqe | {"directed": false, "multigraph": false, "graph": {}, "nodes": [{"id": 0}, {"id": 1}, {"id": 2}, {"id": 3}, {"id": 4}, {"id": 5}, {"id": 6}, {"id": 7}, {"id": 8}], "edges": [{"source": 0, "target": 8}, {"source": 1, "target": 4}, {"source": 1, "target": 6}, {"source": 1, "target": 8}, {"source": 2, "target": 5}, {"sour... | {"states": [338, 342], "expectation_value": -6.252198263872636, "params": [0.39080000000000004, 0.3977, -0.016900000000000002, -0.017400000000000002, 0.3894, 0.39440000000000003, 0.0011, -0.0002, 0.39680000000000004, 0.3911, 0.0022, 0.0026000000000000003, 0.26630000000000004, 0.269, 0.3784, 0.3778, 0.007200000000000001... | 0.5 * (Z(0) @ Z(8)) + 0.5 * (Z(1) @ Z(8)) + 0.5 * (Z(4) @ Z(1)) + 0.5 * (Z(6) @ Z(1)) + 0.5 * (Z(2) @ Z(8)) + 0.5 * (Z(5) @ Z(6)) + 0.5 * (Z(5) @ Z(2)) + 0.5 * (Z(3) @ Z(4)) + 0.5 * (Z(3) @ Z(6)) + 0.5 * (Z(7) @ Z(8)) + 0.5 * (Z(7) @ Z(5)) + 0.5 * (Z(7) @ Z(3)) + -1.5 * Z(8) + 0.0 * Z(0) + -1.0 * Z(1) + -0.5 * Z(4) + -... | 13 | 9 | 4 | {"smallest_eigenvalues": [-6.5], "number_of_smallest_eigenvalues": 1, "first_excited_energy": -5.5, "smallest_bitstrings": ["010101001"], "largest_eigenvalue": 13.5} | OPENQASM 3.0;
include "stdgates.inc";
qubit[9] q;
ry(0.48069105381613647) q[0];
rz(-0.14417519947857718) q[0];
ry(0.213414919954063) q[1];
ry(0.35377341415125907) q[2];
ry(0.4003014525376539) q[3];
ry(0.3766497776353379) q[4];
ry(-0.003329523973467651) q[5];
ry(0.431133191496423) q[6];
ry(0.22089389423062217) q[7];
ry(... | OPENQASM 3.0;
include "stdgates.inc";
input float[64] x0;
input float[64] x1;
input float[64] x10;
input float[64] x100;
input float[64] x101;
input float[64] x102;
input float[64] x103;
input float[64] x104;
input float[64] x105;
input float[64] x106;
input float[64] x107;
input float[64] x108;
input float[64] x109;
i... | null | {"circuits": [], "gradients": []} | [
"ZIIIIIIIZ",
"ZIIIIIIZI",
"IIIIZIIZI",
"IIZIIIIZI",
"ZIIIIIZII",
"IIZZIIIII",
"IIIZIIZII",
"IIIIZZIII",
"IIZIIZIII",
"ZZIIIIIII",
"IZIZIIIII",
"IZIIIZIII",
"ZIIIIIIII",
"IIIIIIIIZ",
"IIIIIIIZI",
"IIIIZIIII",
"IIZIIIIII",
"IIIIIIZII",
"IIIZIIIII",
"IIIIIZIII",
"IZIIIIIII"
] | [
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
0.5,
-1.5,
0,
-1,
-0.5,
-1,
-0.5,
-1,
-1,
-1
] | 0.971385 | [
0.48069105381613647,
0.213414919954063,
0.35377341415125907,
0.4003014525376539,
0.3766497776353379,
-0.003329523973467651,
0.431133191496423,
0.22089389423062217,
0.14804785724852343,
-0.28835039895715436,
-0.09821306197546414,
-0.06830317984104894,
0.2567258798746146,
-0.1645620187829092... | {
"n_parameters": 130,
"n_qubits": 9,
"optimal_eigenvalue": -6.5,
"target_ratio": 0.97,
"target_value": -6.305
} | 11 |
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