Quantum Ground States from Reinforcement Learning

TL;DR

This paper introduces a reinforcement learning method to find quantum ground states by optimizing the drift in a stochastic process, serving as an alternative to traditional path integral Monte Carlo techniques.

Contribution

It presents a novel reinforcement learning framework that learns an optimal importance sampler for Feynman--Kac trajectories to compute quantum ground states.

Findings

Successfully applied to one-, two-, and many-particle systems.

Outperforms traditional Monte Carlo methods in efficiency.

Provides a flexible neural network-based approach for quantum simulations.

Abstract

Finding the ground state of a quantum mechanical system can be formulated as an optimal control problem. In this formulation, the drift of the optimally controlled process is chosen to match the distribution of paths in the Feynman--Kac (FK) representation of the solution of the imaginary time Schr\"odinger equation. This provides a variational principle that can be used for reinforcement learning of a neural representation of the drift. Our approach is a drop-in replacement for path integral Monte Carlo, learning an optimal importance sampler for the FK trajectories. We demonstrate the applicability of our approach to several problems of one-, two-, and many-particle physics.