Classical algorithms for many-body quantum systems at finite energies

TL;DR

This paper presents a hybrid classical approach inspired by quantum algorithms to compute observables in large many-body quantum systems, enabling analysis of bigger systems than traditional methods.

Contribution

It replaces quantum simulation with classical matrix product state techniques in quantum-inspired algorithms, allowing larger system sizes to be studied.

Findings

Successfully simulated spin chains up to 80 sites.

Achieved significant size scalability beyond exact diagonalization.

Demonstrated effectiveness of classical filtering in quantum-inspired algorithms.

Abstract

We investigate quantum inspired algorithms to compute physical observables of quantum many-body systems at finite energies. They are based on the quantum algorithms proposed in [Lu et al. PRX Quantum 2, 020321 (2021)], which use the quantum simulation of the dynamics of such systems, as well as classical filtering and sampling techniques. Here, we replace the quantum simulation by standard classical methods based on matrix product states and operators. As a result, we can address significantly larger systems than those reachable by exact diagonalization or by other algorithms. We demonstrate the performance with spin chains up to 80 sites.