Ground States of Quantum Many Body Lattice Models via Reinforcement Learning

TL;DR

This paper presents a novel reinforcement learning approach to find ground states of quantum lattice models, leveraging stochastic dynamics and neural representations, offering advantages over traditional wavefunction methods.

Contribution

It introduces RL formulations for quantum ground state problems, connecting stochastic dynamics with neural quantum state representations, applicable to both continuous and discrete time models.

Findings

RL can effectively approximate ground states of quantum lattice models

The approach offers advantages over direct wavefunction representations

Applicable to both continuous and discrete time quantum systems

Abstract

We introduce reinforcement learning (RL) formulations of the problem of finding the ground state of a many-body quantum mechanical model defined on a lattice. We show that stoquastic Hamiltonians - those without a sign problem - have a natural decomposition into stochastic dynamics and a potential representing a reward function. The mapping to RL is developed for both continuous and discrete time, based on a generalized Feynman-Kac formula in the former case and a stochastic representation of the Schr\"odinger equation in the latter. We discuss the application of this mapping to the neural representation of quantum states, spelling out the advantages over approaches based on direct representation of the wavefunction of the system.