Quantum-assisted Monte Carlo algorithms for fermions

TL;DR

This paper introduces scalable quantum-assisted Monte Carlo algorithms that leverage minimal quantum resources and Bayesian inference to reduce bias in simulating fermion ground states, enhancing classical methods with quantum advantages.

Contribution

It proposes a family of quantum-assisted Monte Carlo algorithms using Bayesian inference for bias reduction with minimal quantum cost, and demonstrates error suppression in classical ground state calculations.

Findings

Quantum-assisted algorithms reduce bias more efficiently than classical methods.

Bayesian inference enables lower quantum resource requirements.

Hybrid Monte Carlo framework suppresses errors in classical ground state calculations.

Abstract

Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem, for instance, the development of variational quantum algorithms. A recent work by Huggins et al. reports a novel candidate, i.e. a quantum-classical hybrid Monte Carlo algorithm with a reduced bias in comparison to its fully-classical counterpart. In this paper, we propose a family of scalable quantum-assisted Monte Carlo algorithms where the quantum computer is used at its minimal cost and still can reduce the bias. By incorporating a Bayesian inference approach, we can achieve this quantum-facilitated bias reduction with a much smaller quantum-computing cost than taking empirical mean in amplitude estimation. Besides, we show that the hybrid Monte Carlo framework is a general way to suppress errors in the ground state obtained from classical algorithms. Our work provides a Monte Carlo toolkit for achieving quantum-enhanced calculation of fermion systems on near-term quantum devices.