Non-Equilibrium Dynamics of Hybrid Continuous-Discrete Ground-State Sampling

TL;DR

This paper introduces a hybrid continuous-discrete algorithm combining deterministic dynamics with Metropolis-Hastings steps to efficiently sample ground states in complex energy landscapes, showing significant speedups over traditional methods.

Contribution

It presents a novel hybrid framework that integrates continuous-time dynamics with Metropolis-Hastings, improving ground-state sampling efficiency in rugged landscapes.

Findings

MH-driven dynamics reach ground states faster.

Hybrid algorithm achieves 100x speedup on GPUs.

Significant improvements in convergence and accuracy.

Abstract

We propose a general framework for a hybrid continuous-discrete algorithm that integrates continuous-time deterministic dynamics with Metropolis-Hastings steps to combine search dynamics with and without detailed balance. Our purpose is to study the non-equilibrium dynamics that leads to the ground state of rugged energy landscapes in this general setting. Our results show that MH-driven dynamics reach ``easy'' ground states faster, indicating a stronger bias in the non-equilibrium dynamics of the algorithm with reversible transition probabilities. To validate this, we construct a set of Ising problem instances with a controllable bias in the energy landscape that makes one degenerate solution more accessible than another. The constructed hybrid algorithm demonstrates significant improvements in convergence and ground-state sampling accuracy, achieving a 100x speedup on GPUs compared to simulated annealing, making it well-suited for large-scale applications.