Self-Avoiding Random Dynamics on Integer Complex Systems

TL;DR

The paper presents SARDONICS, a novel Monte Carlo sampling algorithm using self-avoiding walks to efficiently explore large state spaces in binary systems, with automatic parameter tuning via Bayesian optimization.

Contribution

Introduction of SARDONICS, a new algorithm for equilibrium sampling that enables large moves in state space and automatic parameter tuning.

Findings

Performs well on Ising models and Boltzmann machines.

Efficiently flips many bits in a single step.

Automatically tunes parameters with Bayesian optimization.

Abstract

This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the algorithm SARDONICS, an acronym for Self-Avoiding Random Dynamics on Integer Complex Systems. The algorithm has several free parameters, but we show that Bayesian optimization can be used to automatically tune them. SARDONICS performs remarkably well in a broad number of sampling tasks: toroidal ferromagnetic and frustrated Ising models, 3D Ising models, restricted Boltzmann machines and chimera graphs arising in the design of quantum computers.