Boltzmann Reinforcement Learning for Noise resilience in Analog Ising Machines

2026-02-09

AI Summary

This work addresses the vulnerability of Analog Ising Machines (AIMs) to measurement noise in combinatorial optimization, which severely degrades the performance of conventional sampling and optimization methods. To overcome this limitation, the authors propose the BRAIN framework, which introduces variational reinforcement learning to AIMs for the first time. By aggregating information from multiple noisy measurements across rounds, BRAIN efficiently approximates the target Boltzmann distribution without requiring state-by-state sampling. This approach substantially enhances robustness to noise while accurately capturing phase transitions and metastable states. Experimental results demonstrate that under 3% Gaussian noise, BRAIN achieves a ground-state fidelity of 98%—compared to only 51% for Markov Chain Monte Carlo—while accelerating computation by 192×, scaling to systems with up to 65,536 spins, and maintaining stable optimization performance even under noise levels as high as 40%.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Quantum Machine Learning
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

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.

Problem

• Analog Ising Machines
• measurement noise
• combinatorial optimization
• Boltzmann distribution
• noise resilience

Innovation

• Boltzmann Reinforcement Learning
• Analog Ising Machines
• Noise Resilience
• Variational Reinforcement Learning
• Combinatorial Optimization