Synergetic quantum error mitigation by randomized compiling and zero-noise extrapolation for the variational quantum eigensolver

TL;DR

This paper introduces a combined error mitigation approach for VQE that uses randomized compiling and zero-noise extrapolation to significantly reduce errors caused by coherent noise, improving accuracy in quantum chemistry simulations.

Contribution

The paper presents a novel combination of randomized compiling and zero-noise extrapolation to effectively mitigate coherent errors in VQE, demonstrated through numerical simulations.

Findings

Mitigates energy errors by up to two orders of magnitude

Effectively converts coherent errors into stochastic errors

Enhances VQE accuracy for small molecule simulations

Abstract

We propose a quantum error mitigation strategy for the variational quantum eigensolver (VQE) algorithm. We find, via numerical simulation, that very small amounts of coherent noise in VQE can cause substantially large errors that are difficult to suppress by conventional mitigation methods, and yet our proposed mitigation strategy is able to significantly reduce these errors. The proposed strategy is a combination of previously reported techniques, namely randomized compiling (RC) and zero-noise extrapolation (ZNE). Intuitively, randomized compiling turns coherent errors in the circuit into stochastic Pauli errors, which facilitates extrapolation to the zero-noise limit when evaluating the cost function. Our numerical simulation of VQE for small molecules shows that the proposed strategy can mitigate energy errors induced by various types of coherent noise by up to two orders of magnitude.