Accurate Learning of Equivariant Quantum Systems from a Single Ground State

TL;DR

This paper introduces a highly efficient method to predict properties of all ground states in quantum systems with periodic boundaries using only a single ground state sample, with proven accuracy improvements.

Contribution

It presents a novel approach to learn all ground state properties from one sample, significantly enhancing efficiency over previous algorithms.

Findings

Prediction error approaches zero in the thermodynamic limit

Method is numerically verified to be effective

Applicable to systems with periodic boundary conditions

Abstract

Predicting properties across system parameters is an important task in quantum physics, with applications ranging from molecular dynamics to variational quantum algorithms. Recently, provably efficient algorithms to solve this task for ground states within a gapped phase were developed. Here we dramatically improve the efficiency of these algorithms by showing how to learn properties of all ground states for systems with periodic boundary conditions from a single ground state sample. We prove that the prediction error tends to zero in the thermodynamic limit and numerically verify the results.