Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer

TL;DR

This paper presents a new quantum algorithm that accelerates quantum Monte Carlo simulations on noisy quantum computers by mitigating errors and easing the sign problem, enabling practical applications on near-term hardware.

Contribution

It introduces a non-variational quantum algorithm that uses shallow circuits and error mitigation to significantly reduce Monte Carlo variance despite noise.

Findings

Reduces Monte Carlo variance by several orders of magnitude

Applicable to near-term noisy quantum hardware

Eases the sign problem in quantum Monte Carlo simulations

Abstract

Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems and real time dynamics. In this paper, we introduce a novel non-variational algorithm using quantum simulation as a subroutine to accelerate quantum Monte Carlo by easing the sign problem. The quantum subroutine can be implemented with shallow circuits and, by incorporating error mitigation, can reduce the Monte Carlo variance by several orders of magnitude even when the circuit noise is significant. As such, the proposed quantum algorithm is applicable to near-term noisy quantum hardware.