iterative low-order decoding

This work addresses the challenges posed by high-order interactions in Ising-based quantum error correction joint decoding, which suffers from poor convergence, substantial computational overhead, and complex hardware embedding. The authors propose an Iterative Low-Order Decoding (ILOD) algorithm that alternately optimizes X-type and Z-type sub-Hamiltonians while incorporating a Bayesian prior to approximate cross-type error correlations, effectively reducing eight- or ten-body interactions to four- or five-body terms. This approach significantly improves convergence, reduces runtime—scaling as (0.81)ᵈ with code distance d—and lowers spin embedding overhead. On the surface code, ILOD achieves a threshold of 4.73%, closely approaching the 4.83% of full joint decoding, and demonstrates stable convergence on large-distance 6.6.6 color codes where joint decoding fails.

To address the challenge of efficiently modeling higher-order interactions in complex systems—particularly protein sequences—this work establishes a rigorous theoretical mapping from restricted Boltzmann machines (RBMs) to the generalized Potts model, yielding the first exact analytical correspondence between the two frameworks. Building on this equivalence, we develop an efficient algorithm grounded in the large-𝑁 statistical approximation, enabling analytical extraction of arbitrary-order effective couplings (e.g., pairwise, three-body). Additionally, we introduce a gauge-fixing formalism to enhance the robustness of parameter estimation. On synthetic data, our method accurately recovers multi-order interactions. When applied to real protein family alignments, it achieves contact map prediction accuracy comparable to state-of-the-art inverse Potts methods. This work thus provides a novel, principled paradigm for modeling higher-order biological networks.

This work addresses the challenge of modeling high-order (third-order and beyond) correlations in discrete high-dimensional data by introducing a class of q-state spin maximum entropy models that incorporate arbitrary high-order and long-range interactions, generalizing binary high-order minimal complexity models to the general discrete setting. Leveraging discrete Fourier analysis and gauge transformations, the study reveals a unified structural equivalence among interaction models of different orders under gauge symmetry. Furthermore, by deriving a closed-form expression for marginal likelihood via a loop expansion of the partition function, the method enables efficient model selection. Empirical validation on multiple real-world datasets demonstrates both the effectiveness of the approach in capturing high-order dependencies and its computational advantages.

This study addresses the optimization and sampling efficiency bottlenecks arising from the absence of hardware-software co-design in Ising machines by proposing a top-down co-design framework. Methodologically, it systematically reviews cross-platform probabilistic algorithms—including simulated annealing, parallel tempering, cluster mean-field, and variational samplers—while deeply integrating the classical QAOA-analogous PAOA algorithm with large language model inference techniques and probabilistic hardware. This integration reveals a bidirectional enhancement mechanism between generative AI and Ising machines. The primary contribution lies in establishing a co-design theoretical framework that accelerates the capability evolution and widespread adoption of next-generation Ising machines, significantly expanding the scale of tractable problems.

This study addresses the problem of selecting optimal Ising or QUBO formulations for maximum-likelihood decoding of linear codes on neuromorphic hardware. Through a systematic comparison of two modeling approaches, it presents the first evaluation within a neuromorphic computing framework of their trade-offs in terms of neuron count, synaptic density, locality, and convergence behavior. The findings demonstrate that ensuring ground-state correctness alone is insufficient to guide practical hardware-aware design; instead, the problem formulation and solver architecture must be co-optimized. By revealing fundamental differences among Ising representations in hardware implementation, this work establishes new design principles for neuromorphic receivers.

研究利用稀疏性解决高维度下的伊辛模型采样及贝叶斯稀疏线性回归问题，提出新的高效采样方法。

This work studies efficient learning of the structure and parameters of Ising models under a more natural observation model: only configurations actually realized during Markov chain evolution are observed—contrary to the standard assumption of observing all update attempts, including rejected (no-change) proposals. For this weak-observation setting, we propose the first polynomial-time algorithm applicable to general reversible single-site update chains, including Metropolis–Hastings chains. Our method leverages robust statistical properties of reversible chains and integrates high-dimensional sparse graph recovery with parameter estimation techniques. For Ising models with maximum degree $d$, our algorithm exactly reconstructs the dependency graph in $mathsf{poly}(d) cdot n^2 log n$ time and estimates parameters in $widetilde{O}(2^d n)$ time, achieving accuracy comparable to optimal full-trajectory methods. This significantly enhances learnability and practicality in realistic dynamic settings.

This work addresses the challenge of efficiently solving NP-hard Ising and Max-Cut problems, where conventional methods struggle due to the complex, non-convex energy landscapes. The authors propose a data-driven iterative dynamical system that parameterizes spin update rules via a shared node-level multilayer perceptron and trains it using zeroth-order optimization to circumvent gradient instability associated with backpropagation. Remarkably, with an extremely low number of parameters, the learned dynamics automatically exhibit momentum-like behavior and time-varying scheduling mechanisms, substantially enhancing search efficiency. Evaluated on standard Ising and combinatorial optimization benchmarks, the method achieves solution quality and convergence speed comparable to state-of-the-art learning-based approaches and classical Ising machine heuristics.

This work investigates how variable encoding—Ising ({−1, +1}) versus QUBO ({0, 1})—affects learning performance, information-geometric structure, and finite-time dynamics of Boltzmann machines. Through theoretical analysis and empirical experiments, we show that QUBO encoding introduces strong cross-terms, rendering the Fisher information matrix ill-conditioned and severely degrading stochastic gradient descent (SGD) convergence; in contrast, Ising encoding enables faster SGD convergence. We further prove that natural gradient descent eliminates encoding dependence, yielding geometrically invariant learning dynamics. Leveraging the intrinsic relationship between the Fisher information matrix and the covariance of sufficient statistics, we derive principled criteria for encoding selection and preprocessing: QUBO-encoded models require centering or preconditioning to match Ising performance. This is the first systematic study to reveal how discrete variable representations fundamentally shape information geometry and optimization trajectories, providing both theoretical foundations and practical guidelines for encoding design in probabilistic models.

Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample configurations generated from the model. For many systems of interest that arise in physical contexts, expecting a full sample to be observed is not practical, and hence it is important to look for computationally efficient methods that solve the learning problem with access to only a limited set of statistics. We examine the trade-offs between the power of computation and observation within this scenario, employing the Ising model as a paradigmatic example. We demonstrate that it is feasible to reconstruct the model parameters for a model with $\ell_1$ width $\gamma$ by observing statistics up to an order of $O(\gamma)$. This approach allows us to infer the model's structure and also learn its couplings and magnetic fields. We also discuss a setting where prior information about structure of the model is available and show that the learning problem can be solved efficiently with even more limited observational power.