Daily Papers

We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by sequences of elementary braids of quasiparticles with exotic fractional statistics in certain two-dimensional topological condensed matter systems, described by effective topological quantum field theories. We specifically focus on a non-semisimple version of topological field theory, which provides a foundation for an extended theory of Ising anyons and which has recently been shown by Iulianelli et al., Nature Communications {\bf 16}, 6408 (2025), to permit universal quantum computation. While the proofs of this pioneering result are existential in nature, the mixed integer programming provides an approach to explicitly construct quantum gates in topological systems. We demonstrate this by focusing specifically on the entangling controlled-NOT operation, and its local equivalence class, using braiding operations in the non-semisimple Ising system. This illustrates the utility of the Mixed-Integer Quadratically Constrained Quadratic Programming for topological quantum compilation.

We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we implement and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The practical tools provided in this work allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

Autonomous wire harness assembly requires robots to manipulate complex branched cables with high precision and reliability. A key challenge in automating this process is predicting how these flexible and branched structures behave under manipulation. Without accurate predictions, it is difficult for robots to reliably plan or execute assembly operations. While existing research has made progress in modeling single-threaded Deformable Linear Objects (DLOs), extending these approaches to Branched Deformable Linear Objects (BDLOs) presents fundamental challenges. The junction points in BDLOs create complex force interactions and strain propagation patterns that cannot be adequately captured by simply connecting multiple single-DLO models. To address these challenges, this paper presents Differentiable discrete branched Elastic rods for modeling Furcated DLOs in real-Time (DEFT), a novel framework that combines a differentiable physics-based model with a learning framework to: 1) accurately model BDLO dynamics, including dynamic propagation at junction points and grasping in the middle of a BDLO, 2) achieve efficient computation for real-time inference, and 3) enable planning to demonstrate dexterous BDLO manipulation. A comprehensive series of real-world experiments demonstrates DEFT's efficacy in terms of accuracy, computational speed, and generalizability compared to state-of-the-art alternatives. Project page:https://roahmlab.github.io/DEFT/.

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault-tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of appendices in which we provide supplementary information to the main text.

We study the problem of learning to perform multi-stage robotic manipulation tasks, with applications to cable routing, where the robot must route a cable through a series of clips. This setting presents challenges representative of complex multi-stage robotic manipulation scenarios: handling deformable objects, closing the loop on visual perception, and handling extended behaviors consisting of multiple steps that must be executed successfully to complete the entire task. In such settings, learning individual primitives for each stage that succeed with a high enough rate to perform a complete temporally extended task is impractical: if each stage must be completed successfully and has a non-negligible probability of failure, the likelihood of successful completion of the entire task becomes negligible. Therefore, successful controllers for such multi-stage tasks must be able to recover from failure and compensate for imperfections in low-level controllers by smartly choosing which controllers to trigger at any given time, retrying, or taking corrective action as needed. To this end, we describe an imitation learning system that uses vision-based policies trained from demonstrations at both the lower (motor control) and the upper (sequencing) level, present a system for instantiating this method to learn the cable routing task, and perform evaluations showing great performance in generalizing to very challenging clip placement variations. Supplementary videos, datasets, and code can be found at https://sites.google.com/view/cablerouting.

The higher Bruhat orders B(n,k) were introduced by Manin-Schechtman to study discriminantal hyperplane arrangements and subsequently studied by Ziegler, who connected B(n,k) to oriented matroids. In this paper, we consider the enumeration of B(n,k) and improve upon Balko's asymptotic lower and upper bounds on |B(n,k)| by a factor exponential in k. A proof of Ziegler's formula for |B(n,n-3)| is given and a bijection between a certain subset of B(n,n-4) and totally symmetric plane partitions is proved. Central to our proofs are deletion and contraction operations for the higher Bruhat orders, defined in analogy with matroids. Dual higher Bruhat orders are also introduced, and we construct isomorphisms relating the higher Bruhat orders and their duals. Additionally, weaving functions are introduced to generalize Felsner's encoding of elements in B(n,2) to all higher Bruhat orders B(n,k).

We introduce a Heegaard-Floer homology functor from the category of oriented links in closed 3-manifolds and oriented surface cobordisms in 4-manifolds connecting them to the category of F[v]-modules and F[v]-homomorphisms between them, where F is the field with two elements. In comparison with previously defined TQFTs for decorated links and link cobordisms, the construction of this paper has the advantage of being independent from the decoration. Some of the basic properties of this functor are also explored.

We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.

Rigged 3D assets are fundamental to 3D deformation and animation. However, existing 3D generation methods face challenges in generating animatable geometry, while rigging techniques lack fine-grained structural control over skeleton creation. To address these limitations, we introduce Stroke3D, a novel framework that directly generates rigged meshes from user inputs: 2D drawn strokes and a descriptive text prompt. Our approach pioneers a two-stage pipeline that separates the generation into: 1) Controllable Skeleton Generation, we employ the Skeletal Graph VAE (Sk-VAE) to encode the skeleton's graph structure into a latent space, where the Skeletal Graph DiT (Sk-DiT) generates a skeletal embedding. The generation process is conditioned on both the text for semantics and the 2D strokes for explicit structural control, with the VAE's decoder reconstructing the final high-quality 3D skeleton; and 2) Enhanced Mesh Synthesis via TextuRig and SKA-DPO, where we then synthesize a textured mesh conditioned on the generated skeleton. For this stage, we first enhance an existing skeleton-to-mesh model by augmenting its training data with TextuRig: a dataset of textured and rigged meshes with captions, curated from Objaverse-XL. Additionally, we employ a preference optimization strategy, SKA-DPO, guided by a skeleton-mesh alignment score, to further improve geometric fidelity. Together, our framework enables a more intuitive workflow for creating ready to animate 3D content. To the best of our knowledge, our work is the first to generate rigged 3D meshes conditioned on user-drawn 2D strokes. Extensive experiments demonstrate that Stroke3D produces plausible skeletons and high-quality meshes.

We introduce Mesh Silksong, a compact and efficient mesh representation tailored to generate the polygon mesh in an auto-regressive manner akin to silk weaving. Existing mesh tokenization methods always produce token sequences with repeated vertex tokens, wasting the network capability. Therefore, our approach tokenizes mesh vertices by accessing each mesh vertice only once, reduces the token sequence's redundancy by 50\%, and achieves a state-of-the-art compression rate of approximately 22\%. Furthermore, Mesh Silksong produces polygon meshes with superior geometric properties, including manifold topology, watertight detection, and consistent face normals, which are critical for practical applications. Experimental results demonstrate the effectiveness of our approach, showcasing not only intricate mesh generation but also significantly improved geometric integrity.

We explore the effects of various plasticity functions on assemblies of neurons. To bridge the gap between experimental and computational theories we make use of a conceptual framework, the Assembly Calculus, which is a formal system for the description of brain function based on assemblies of neurons. The Assembly Calculus includes operations for projecting, associating, and merging assemblies of neurons. Our research is focused on simulating different plasticity functions with Assembly Calculus. Our main contribution is the modification and evaluation of the projection operation. We experiment with Oja's and Spike Time-Dependent Plasticity (STDP) rules and test the effect of various hyper-parameters.

Manipulation of deformable objects, such as ropes and cloth, is an important but challenging problem in robotics. We present a learning-based system where a robot takes as input a sequence of images of a human manipulating a rope from an initial to goal configuration, and outputs a sequence of actions that can reproduce the human demonstration, using only monocular images as input. To perform this task, the robot learns a pixel-level inverse dynamics model of rope manipulation directly from images in a self-supervised manner, using about 60K interactions with the rope collected autonomously by the robot. The human demonstration provides a high-level plan of what to do and the low-level inverse model is used to execute the plan. We show that by combining the high and low-level plans, the robot can successfully manipulate a rope into a variety of target shapes using only a sequence of human-provided images for direction.

The shift towards electrification and autonomous driving in the automotive industry results in more and more automotive wire harnesses being installed in modern automobiles, which stresses the great significance of guaranteeing the quality of automotive wire harness assembly. The mating of connectors is essential in the final assembly of automotive wire harnesses due to the importance of connectors on wire harness connection and signal transmission. However, the current manual operation of mating connectors leads to severe problems regarding assembly quality and ergonomics, where the robotized assembly has been considered, and different vision-based solutions have been proposed to facilitate a better perception of the robot control system on connectors. Nonetheless, there has been a lack of deep learning-based solutions for detecting automotive wire harness connectors in previous literature. This paper presents a deep learning-based connector detection for robotized automotive wire harness assembly. A dataset of twenty automotive wire harness connectors was created to train and evaluate a two-stage and a one-stage object detection model, respectively. The experiment results indicate the effectiveness of deep learning-based connector detection for automotive wire harness assembly but are limited by the design of the exteriors of connectors.

Fully Homomorphic Encryption (FHE) is an encryption scheme that allows for computation to be performed directly on encrypted data, effectively closing the loop on secure and outsourced computing. Data is encrypted not only during rest and transit, but also during processing. However, FHE provides a limited instruction set: SIMD addition, SIMD multiplication, and cyclic rotation of 1-D vectors. This restriction makes performing multi-dimensional tensor operations challenging. Practitioners must pack these tensors into 1-D vectors and map tensor operations onto this one-dimensional layout rather than their traditional nested structure. And while prior systems have made significant strides in automating this process, they often hide critical packing decisions behind layers of abstraction, making debugging, optimizing, and building on top of these systems difficult. In this work, we approach multi-dimensional tensor operations in FHE through Einstein summation (einsum) notation. Einsum notation explicitly encodes dimensional structure and operations in its syntax, naturally exposing how tensors should be packed and transformed. We decompose einsum expressions into a fixed set of FHE-friendly operations. We implement our design and present EinHops, a minimalist system that factors einsum expressions into a fixed sequence of FHE operations. EinHops enables developers to perform encrypted tensor operations using FHE while maintaining full visibility into the underlying packing strategy. We evaluate EinHops on a range of tensor operations from a simple transpose to complex multi-dimensional contractions. We show that the explicit nature of einsum notation allows us to build an FHE tensor system that is simple, general, and interpretable. We open-source EinHops at the following repository: https://github.com/baahl-nyu/einhops.

We explore whether surgical manipulation tasks can be learned on the da Vinci robot via imitation learning. However, the da Vinci system presents unique challenges which hinder straight-forward implementation of imitation learning. Notably, its forward kinematics is inconsistent due to imprecise joint measurements, and naively training a policy using such approximate kinematics data often leads to task failure. To overcome this limitation, we introduce a relative action formulation which enables successful policy training and deployment using its approximate kinematics data. A promising outcome of this approach is that the large repository of clinical data, which contains approximate kinematics, may be directly utilized for robot learning without further corrections. We demonstrate our findings through successful execution of three fundamental surgical tasks, including tissue manipulation, needle handling, and knot-tying.

High-reliability long-horizon robotic manipulation has traditionally relied on large-scale data and compute to understand complex real-world dynamics. However, we identify that the primary bottleneck to real-world robustness is not resource scale alone, but the distributional shift among the human demonstration distribution, the inductive bias learned by the policy, and the test-time execution distribution -- a systematic inconsistency that causes compounding errors in multi-stage tasks. To mitigate these inconsistencies, we propose χ_{0}, a resource-efficient framework with effective modules designated to achieve production-level robustness in robotic manipulation. Our approach builds off three technical pillars: (i) Model Arithmetic, a weight-space merging strategy that efficiently soaks up diverse distributions of different demonstrations, varying from object appearance to state variations; (ii) Stage Advantage, a stage-aware advantage estimator that provides stable, dense progress signals, overcoming the numerical instability of prior non-stage approaches; and (iii) Train-Deploy Alignment, which bridges the distribution gap via spatio-temporal augmentation, heuristic DAgger corrections, and temporal chunk-wise smoothing. χ_{0} enables two sets of dual-arm robots to collaboratively orchestrate long-horizon garment manipulation, spanning tasks from flattening, folding, to hanging different clothes. Our method exhibits high-reliability autonomy; we are able to run the system from arbitrary initial state for consecutive 24 hours non-stop. Experiments validate that χ_{0} surpasses the state-of-the-art π_{0.5} in success rate by nearly 250%, with only 20-hour data and 8 A100 GPUs. Code, data and models will be released to facilitate the community.

Gross, Mansour, and Tucker introduced the partial-duality polynomial of a ribbon graph [Distributions, European J. Combin. 86, 1--20, 2020], the generating function enumerating partial duals by the Euler genus. Chmutov and Vignes-Tourneret wondered if this polynomial and its conjectured properties would hold for general delta-matroids, which are combinatorial abstractions of ribbon graphs. Yan and Jin contributed to this inquiry by identifying a subset of delta-matroids-specifically, even normal binary ones-whose twist polynomials are characterized by a singular term. Building upon this foundation, the current paper expands the scope of the investigation to encompass even non-binary delta-matroids, revealing that none of them have width-changing twists.

In 1983, Gromov introduced the notion of distortion of a knot, and asked if there are knots with arbitrarily large distortion. In 2011, Pardon proved that the distortion of T_{p,q} is at least min{p,q} up to a constant factor. We prove that the distortion of T_{p, p+1}# K is at least p up to a constant, independent of K. We also prove that any embedding of a minimal genus Seifert surface for T_{p,p+1}# K in R^3 has small extrinsic systole, in the sense that it contains a non-contractible loop with small R^3-diameter relative to the length of the knot. These results are related to combinatorial properties of the monodromy map associated to torus knots.

Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation schemes, logical circuits are compiled following a place-and-route paradigm, where logical qubits remain statically fixed in space throughout the computation. In this work, we introduce a paradigm shift by exploiting movable logical qubits via teleportation during the logical lattice surgery CNOT gate. Focusing on lattice surgery with the color code, we propose a proof-of-concept compilation scheme that leverages this capability. Numerical simulations show that the proposed approach can substantially reduce the routed circuit depth compared to standard place-and-route compilation techniques. Our results demonstrate that optimizations based on movable logical qubits are not limited to architectures with physically movable qubits, such as neutral atoms or trapped ions - they are also readily applicable to superconducting quantum hardware. An open-source implementation of our method is available on GitHub https://github.com/munich-quantum-toolkit/qecc.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

We prove that the homotopy limits and homotopy colimits of chain complexes can be computed by the cobar and bar constructions. We also show that the totalizations of double complexes compute the homotopy limits and homotopy colimits of simplicial and cosimplicial chain complexes.

Fine manipulation tasks, such as threading cable ties or slotting a battery, are notoriously difficult for robots because they require precision, careful coordination of contact forces, and closed-loop visual feedback. Performing these tasks typically requires high-end robots, accurate sensors, or careful calibration, which can be expensive and difficult to set up. Can learning enable low-cost and imprecise hardware to perform these fine manipulation tasks? We present a low-cost system that performs end-to-end imitation learning directly from real demonstrations, collected with a custom teleoperation interface. Imitation learning, however, presents its own challenges, particularly in high-precision domains: errors in the policy can compound over time, and human demonstrations can be non-stationary. To address these challenges, we develop a simple yet novel algorithm, Action Chunking with Transformers (ACT), which learns a generative model over action sequences. ACT allows the robot to learn 6 difficult tasks in the real world, such as opening a translucent condiment cup and slotting a battery with 80-90% success, with only 10 minutes worth of demonstrations. Project website: https://tonyzhaozh.github.io/aloha/

Leveraging human motion data to impart robots with versatile manipulation skills has emerged as a promising paradigm in robotic manipulation. Nevertheless, translating multi-source human hand motions into feasible robot behaviors remains challenging, particularly for robots equipped with multi-fingered dexterous hands characterized by complex, high-dimensional action spaces. Moreover, existing approaches often struggle to produce policies capable of adapting to diverse environmental conditions. In this paper, we introduce HERMES, a human-to-robot learning framework for mobile bimanual dexterous manipulation. First, HERMES formulates a unified reinforcement learning approach capable of seamlessly transforming heterogeneous human hand motions from multiple sources into physically plausible robotic behaviors. Subsequently, to mitigate the sim2real gap, we devise an end-to-end, depth image-based sim2real transfer method for improved generalization to real-world scenarios. Furthermore, to enable autonomous operation in varied and unstructured environments, we augment the navigation foundation model with a closed-loop Perspective-n-Point (PnP) localization mechanism, ensuring precise alignment of visual goals and effectively bridging autonomous navigation and dexterous manipulation. Extensive experimental results demonstrate that HERMES consistently exhibits generalizable behaviors across diverse, in-the-wild scenarios, successfully performing numerous complex mobile bimanual dexterous manipulation tasks. Project Page:https://gemcollector.github.io/HERMES/.

Garment manipulation is a critical challenge due to the diversity in garment categories, geometries, and deformations. Despite this, humans can effortlessly handle garments, thanks to the dexterity of our hands. However, existing research in the field has struggled to replicate this level of dexterity, primarily hindered by the lack of realistic simulations of dexterous garment manipulation. Therefore, we propose DexGarmentLab, the first environment specifically designed for dexterous (especially bimanual) garment manipulation, which features large-scale high-quality 3D assets for 15 task scenarios, and refines simulation techniques tailored for garment modeling to reduce the sim-to-real gap. Previous data collection typically relies on teleoperation or training expert reinforcement learning (RL) policies, which are labor-intensive and inefficient. In this paper, we leverage garment structural correspondence to automatically generate a dataset with diverse trajectories using only a single expert demonstration, significantly reducing manual intervention. However, even extensive demonstrations cannot cover the infinite states of garments, which necessitates the exploration of new algorithms. To improve generalization across diverse garment shapes and deformations, we propose a Hierarchical gArment-manipuLation pOlicy (HALO). It first identifies transferable affordance points to accurately locate the manipulation area, then generates generalizable trajectories to complete the task. Through extensive experiments and detailed analysis of our method and baseline, we demonstrate that HALO consistently outperforms existing methods, successfully generalizing to previously unseen instances even with significant variations in shape and deformation where others fail. Our project page is available at: https://wayrise.github.io/DexGarmentLab/.

We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is benchmarked against state-of-the-art techniques, showing a remarkable acceleration. As a side product, we provide an optimized method for one key calculus in quantum simulations: the Pauli basis decomposition of Hamiltonians.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.

The ZX-calculus is a universal graphical language for qubit quantum computation, meaning that every linear map between qubits can be expressed in the ZX-calculus. Furthermore, it is a complete graphical rewrite system: any equation involving linear maps that is derivable in the Hilbert space formalism for quantum theory can also be derived in the calculus by rewriting. It has widespread usage within quantum industry and academia for a variety of tasks such as quantum circuit optimisation, error-correction, and education. The ZW-calculus is an alternative universal graphical language that is also complete for qubit quantum computing. In fact, its completeness was used to prove that the ZX-calculus is universally complete. This calculus has advanced how quantum circuits are compiled into photonic hardware architectures in the industry. Recently, by combining these two calculi, a new calculus has emerged for qubit quantum computation, the ZXW-calculus. Using this calculus, graphical-differentiation, -integration, and -exponentiation were made possible, thus enabling the development of novel techniques in the domains of quantum machine learning and quantum chemistry. Here, we generalise the ZXW-calculus to arbitrary finite dimensions, that is, to qudits. Moreover, we prove that this graphical rewrite system is complete for any finite dimension. This is the first completeness result for any universal graphical language beyond qubits.