Boltzmann Reinforcement Learning for Noise resilience in Analog Ising Machines

TL;DR

This paper introduces BRAIN, a reinforcement learning framework that enhances the noise resilience of Analog Ising Machines, enabling accurate optimization and thermodynamic analysis despite measurement noise.

Contribution

BRAIN is a novel distribution learning approach that leverages variational reinforcement learning to improve noise robustness in AIMs for complex combinatorial problems.

Findings

BRAIN maintains 98% ground state fidelity under 3% Gaussian noise.

BRAIN is up to 192 times faster than MCMC under noisy conditions.

BRAIN scales efficiently up to 65,536 spins with robust noise tolerance.

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.