Fighting noise with noise: a stochastic projective quantum eigensolver

TL;DR

This paper introduces a stochastic projective quantum eigensolver that leverages quantum Monte Carlo ideas to reduce quantum resource requirements, enabling more efficient quantum chemistry computations on noisy intermediate-scale quantum devices.

Contribution

It presents a novel stochastic approach to quantum eigensolvers that significantly decreases the sampling needed for accurate ground and excited state calculations.

Findings

Achieves two orders of magnitude reduction in sampling for ground state energy convergence.

Applicable to excited-state calculations with similar efficiency gains.

Offers a promising near-term method for Hamiltonian simulation on noisy quantum devices.

Abstract

In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to non-trivial quantum chemistry problems. In this paper we propose applying some of the fundamental ideas of conventional Quantum Monte Carlo algorithms -- stochastic sampling of both the wavefunction and the Hamiltonian -- to quantum algorithms in order to significantly decrease quantum resource costs. In the context of an imaginary-time propagation based projective quantum eigensolver, we present a novel approach to estimating physical observables which leads to a two order of magnitude reduction in the required sampling of the quantum state to converge the ground state energy of a system relative to current state-of-the-art eigensolvers. The method can be equally applied to excited-state calculations and, combined with stochastic approximations of the system Hamiltonian, provides a promising near-term approach to Hamiltonian simulation for general chemistry on quantum devices.