Reinforcement learning for path integrals in quantum statistical physics

TL;DR

This paper introduces a reinforcement learning approach to compute Euclidean path integrals in quantum statistical physics, enabling efficient calculation of thermal properties and free energy in quantum systems.

Contribution

It presents a novel two-step reinforcement learning method for path integrals, combining variational approximation with exact computation, applied to quantum systems.

Findings

Successfully benchmarked on simple quantum systems

Applied to quantum rotor chain with promising results

Demonstrated efficiency over traditional methods

Abstract

Machine learning is rapidly finding its way into the field of computational quantum physics. One of the most popular and widely studied approaches in this direction is to use neural networks to model quantum states (NQS) in the Hamiltonian formulation of quantum mechanics. However, an alternative angle of attack to leverage machine learning in physics is through the path integral formulation, which has so far received far more limited attention. In this paper, we explore how reinforcement learning can be used to compute a class of Euclidean path integrals that yield the thermal density matrix of a quantum system, thereby enabling the computation of the free energy or other thermal expectation values. In particular, we propose a two-step approach with the unique feature that after a variational approximation for a quantity is obtained in a first step, it can then be used to efficiently compute the exact result in a second step. We benchmark this method on several simple systems and then apply it to the quantum rotor chain.