Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer

TL;DR

This paper introduces a hybrid quantum-classical approach that reduces biases in fermionic quantum Monte Carlo methods, enabling larger and more accurate simulations of many-electron systems on quantum computers.

Contribution

It presents a novel method combining constrained QMC with quantum computing to unbias calculations, demonstrated on systems with up to 120 orbitals.

Findings

Largest chemistry simulations on quantum computers to date

Achieved accuracy comparable to classical state-of-the-art methods

Surpassed variational quantum eigensolver in potential for practical quantum advantage

Abstract

Many-electron problems pose some of the greatest challenges in computational science, with important applications across many fields of modern science. Fermionic quantum Monte Carlo (QMC) methods are among the most powerful approaches to these problems. However, they can be severely biased when controlling the fermionic sign problem using constraints, as is necessary for scalability. Here we propose an approach that combines constrained QMC with quantum computing tools to reduce such biases. We experimentally implement our scheme using up to 16 qubits in order to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed on quantum computers (more than doubling the size of prior electron correlation calculations), while obtaining accuracy competitive with state-of-the-art classical methods. Our results demonstrate a new paradigm of hybrid quantum-classical algorithm, surpassing the popular variational quantum eigensolver in terms of potential towards the first practical quantum advantage in ground state many-electron calculations.