molecular-shadows-h2-v10

Direct observable regressor for fermionic shadow spectroscopy on H2 / STO-3G. Predicts time-evolved expectation values of 28 Majorana observables (\Gamma_\mu(t) = e^{iH(R)t}\Gamma_\mu e^{-iH(R)t}) as a function of bond length (R) and time (t), with the goal of feeding the resulting signal matrix into the Chan et al. shadow-spectroscopy post-processing pipeline to recover energy gaps without expensive quantum-circuit-side time evolution.

Architecture (v10)

(R, t) + HF orbital energies ε(R)
      │
      ├── freq_net(ε(R))  → 256 learnable Fourier frequencies ω_k(R)
      │
      ├── Fourier features [sin(ω_k t), cos(ω_k t)]  (256 × 2 = 512 features)
      │
      └── Trunk MLP: input [R, fourier]  → 6 layers × 768 hidden → 28 outputs

Hyperparameter	Value
n_observables	28 (k=1 Majorana operators on 4 spin-orbitals)
n_fourier	256
trunk depth × width	6 × 768
freq_net depth × width	3 × 128
n_orb_features	2 (HF spatial-orbital energies of H2/STO-3G)
conditioned_frequencies	True
adaptive_bandwidth	False (v10)
activation	GELU
Parameter count	~14 M

Held-out evaluation

50 held-out geometries on the dense (R \in [0.5, 3.0]) Å grid ((\Delta R = 0.01), 251 total). Trained on the remaining 201.

R bin (Å)	n	pearson_mean	pearson_median	range_ratio	MSE
0.65–1.11	11	0.9859	0.9984	0.9893	3.58e-6
1.11–1.56	8	0.9861	0.9980	0.9903	6.19e-6
1.56–2.02	7	0.9918	0.9982	0.9923	7.07e-6
2.02–2.47	12	0.9987	0.9994	0.9988	2.52e-6
2.47–2.93	12	0.9996	0.9997	0.9995	1.42e-6
all	50	0.9931	0.9967	0.9946	3.71e-6

Pearson is per-observable, then averaged across the 28 observables and reported as mean and median of those 28 values for each held-out R.

Inputs / outputs

• Input. (R, t) where R is bond length in Å and t is propagation time in atomic units ((\hbar/E_h)).
• Output. Length-28 vector of expectation values (\langle\psi_0(R)|\Gamma_\mu(t)|\psi_0(R)\rangle) for the 28 k=1 Majorana observables on H2/STO-3G's 4 spin-orbital JW encoding. Initial state (|\psi_0\rangle) is Hartree–Fock with explicit symmetry-breaking excitations to populate non-trivial gap manifolds.
• Valid range. Trained on (R \in [0.5, 3.0]) Å, (t \in [0, 300]) a.u. Extrapolation outside is unsupported.

Quickstart

from huggingface_hub import snapshot_download
from inference import MolecularShadowsRegressor

# token only needed while the repo is private
m = MolecularShadowsRegressor.from_hub(
    "aniketdesh/molecular-shadows-h2-v10",
    revision="v10",                # pin the architecture version
    token="hf_...",
)

import numpy as np
t_grid = np.linspace(0, 300, 1500)
y = m.predict_trajectory(R=1.4, t_grid=t_grid)   # (1500, 28) trajectory at R=1.4 Å

Training data

• Bond-length grid: (R \in [0.5, 3.0]) Å, (\Delta R = 0.01) Å (251 points).
• Time grid: (t \in [0, 300]) a.u., 1500 points ((\Delta\omega \approx 0.021,E_h), (\omega_{\max} \approx 15.7,E_h) Nyquist).
• Initial state: Hartree–Fock with symmetry-breaking excitations.
• Targets: exact ED of H2/STO-3G via PennyLane, observables k=1 Majorana operators.
• Train/test split: 201 / 50, random per-R holdout, seed 42.

Files in this repo

File	Purpose
regressor.pt	torch payload: state_dict + model_config + R/t grids + observable_keys
observable_regressor.py	model architecture (single file, no project deps)
inference.py	MolecularShadowsRegressor.from_local / from_hub loader
orbital_energies.npz	R-grid + HF orbital-energy table for inference-time interpolation
eval_results.json	per-R held-out eval metrics (50 geometries)
eval_summary.json	aggregate metrics
history.json	training loss / val MSE curves
README.md	this file

Versioning

• v10 (current): HF orbital-energy freq_net + dense R-grid + 6×768 trunk. Mean Pearson 0.993 across the full PES.
• Future versions (v11+) will be pushed as new commits on main with new tags. Pin via revision="v10" to preserve loading across architecture changes; main always tracks the latest.

Citation

Method: matchgate-shadow spectroscopy following arXiv:2212.11036 and matchgate-shadow theory.

Code and training pipeline are research-internal; please contact for citation text once the manuscript is on arXiv.

License

MIT.