Accelerated Stochastic Sampling of Discrete Statistical Systems

TL;DR

This paper introduces a novel method to accelerate stochastic sampling in discrete statistical systems by transforming the master equation into an imaginary-time Schrödinger equation, significantly reducing relaxation times and improving optimization processes.

Contribution

The paper generalizes an acceleration technique from continuous to discrete systems using a master equation approach, enhancing sampling efficiency in complex energy landscapes.

Findings

Achieved an order of magnitude speedup in simulated annealing for the traveling salesman problem.

Demonstrated improved sampling efficiency compared to traditional methods.

Validated the approach against exchange Monte Carlo in spin glass simulations.

Abstract

We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for continuous systems. The method starts from a master equation, in contrast to the Fokker-Planck equation for the continuous case. The master equation is transformed into an imaginary-time Schr\"odinger equation. The Hamiltonian of the Schr\"odinger equation is modified by adding a projector to its known ground state. We show how this transformation decreases the relaxation time and propose a way to use it to accelerate simulated annealing for optimization problems. We implement our method in a simplified kinetic Monte Carlo scheme and show an acceleration by an order of magnitude in simulated annealing of the symmetric traveling salesman problem. Comparisons of simulated annealing are made with the exchange Monte Carlo algorithm for the three-dimensional Ising spin glass. Our implementation can be seen as a step toward accelerating the stochastic sampling of generic systems with complex landscapes and long equilibration times.