Unbiasing fermionic quantum Monte Carlo with a quantum computer

William J Huggins,Bryan A O’Gorman,Ryan Babbush,Joonho Lee,David R Reichman,Nicholas C Rubin

doi:10.1038/s41586-021-04351-z

William J Huggins, Bryan A O’Gorman + Show 4 more

Open Access

https://doi.org/10.1038/s41586-021-04351-z

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Abstract

Interacting many-electron problems pose some of the greatest computational challenges in science, with essential applications across many fields. The solutions to these problems will offer accurate predictions of chemical reactivity and kinetics, and other properties of quantum systems1–4. Fermionic quantum Monte Carlo (QMC) methods5,6, which use a statistical sampling of the ground state, are among the most powerful approaches to these problems. Controlling the fermionic sign problem with constraints ensures the efficiency of QMC at the expense of potentially significant biases owing to the limited flexibility of classical computation. Here we propose an approach that combines constrained QMC with quantum computation to reduce such biases. We implement our scheme experimentally using up to 16 qubits to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed with the help of quantum computers, while achieving accuracy that is competitive with state-of-the-art classical methods without burdensome error mitigation. Compared with the popular variational quantum eigensolver7,8, our hybrid quantum-classical computational model offers an alternative path towards achieving a practical quantum advantage for the electronic structure problem without demanding exceedingly accurate preparation and measurement of the ground-state wavefunction.

Highlights

Throughout the time evolution, queries to the quantum processor about the overlap value between the quantum trial wavefunction|ΨT⟩and a stochastic wavefunction sample{|φi⟩}τ are made while updating the gate parameters to describe{|φi⟩}τ
Our quantum processor uses N qubits to efficiently estimate the overlap, which is used to evolve wi and to discard stochastic wavefunction samples with wi < 0. Observables, such as E(τ ), are computed on the classical computer using overlap queries to the quantum processor (Supplementary Section C)
In quantum Monte Carlo (QMC), the imaginary-time evolution in equation (1) is implemented stochastically, which can enable a polynomial scaling algorithm to sample an estimate for the exact ground-state energy by avoiding the explicit storage of high-dimensional objects, such as Hand Ψ0

Summary

Introduction

Quantum computing has arisen as an alternative model for the calculation of quantum properties that may complement, and potentially surpass, classical methods in terms of efficiency[9,10]. We do not attempt to represent the ground-state wavefunction using our quantum processor, choosing instead to use it to guide a quantum Monte Carlo (QMC) calculation performed on a classical coprocessor. Using this approach, our experimental demonstration surpasses the scale of previous experimental work on quantum simulation in chemistry[15–17]. In QMC, the imaginary-time evolution in equation (1) is implemented stochastically, which can enable a polynomial scaling algorithm to sample an estimate for the exact ground-state energy by avoiding the explicit storage of high-dimensional objects, such as Hand Ψ0. Exact, unbiased QMC approaches are only applicable to small systems[19–21] or those lacking a sign problem[22]

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