Quantum-Inspired Tempering for Ground State Approximation using Artificial Neural Networks

TL;DR

This paper introduces a quantum-inspired parallel tempering method for training artificial neural networks to better approximate ground states of quantum many-body systems, overcoming local minima traps in standard algorithms.

Contribution

It proposes a novel parallel tempering approach for neural network training, inspired by quantum parallel tempering, to improve ground state approximation in complex quantum systems.

Findings

Enhanced ability to escape local minima during training.

Successful application to permutation-invariant Hamiltonians.

Effective in electronic structure problems with false minima.

Abstract

A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem's small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.