Boltzmann Reinforcement Learning for Noise resilience in Analog Ising Machines

Analog Ising machines (AIMs) have emerged as a promising paradigm for combinatorial optimization, utilizing physical dynamics to solve Ising problems with high energy efficiency. However, the performance of traditional optimization and sampling algorithms on these platforms is often limited by inherent measurement noise. We introduce BRAIN (Boltzmann Reinforcement for Analog Ising Networks), a distribution learning framework that utilizes variational reinforcement learning to approximate the Boltzmann distribution. By shifting from state-by-state sampling to aggregating information across multiple noisy measurements, BRAIN is resilient to Gaussian noise characteristic of AIMs. We evaluate BRAIN across diverse combinatorial topologies, including the Curie-Weiss and 2D nearest-neighbor Ising systems. We find that under realistic 3% Gaussian measurement noise, BRAIN maintains 98% ground state fidelity, whereas Markov Chain Monte Carlo (MCMC) methods degrade to 51% fidelity. Furthermore, BRAIN reaches the MCMC-equivalent solution up to 192x faster under these conditions. BRAIN exhibits $\mathcal{O}(N^{1.55})$ scaling up to 65,536 spins and maintains robustness against severe measurement uncertainty up to 40%. Beyond ground state optimization, BRAIN accurately captures thermodynamic phase transitions and metastable states, providing a scalable and noise-resilient method for utilizing analog computing architectures in complex optimizations.

💡 Research Summary

The paper introduces BRAIN (Boltzmann Reinforcement for Analog Ising Networks), a variational reinforcement‑learning framework designed specifically for the noisy, sequential nature of analog Ising machines (AIMs). AIMs exploit physical dynamics (optical or electronic oscillators) to solve Ising‑type combinatorial problems with orders‑of‑magnitude speedups over digital processors, but their measurements are corrupted by 3–10 % Gaussian noise and provide only non‑differentiable energy scores. Traditional sampling methods such as Markov‑Chain Monte Carlo (MCMC) rely on precise energy differences to maintain detailed balance; when noise approaches the scale of ΔE, acceptance becomes essentially random and convergence fails.

BRAIN addresses these constraints by (1) representing the target distribution with a fully factorized Bernoulli policy qθ(x)=∏j mj^{(1+xj)/2}(1‑mj)^{(1‑xj)/2}, where each spin j has an independent probability mj∈