Mitigating Quantum Gate Errors for Variational Eigensolvers Using Hardware-Inspired Zero-Noise Extrapolation

TL;DR

This paper presents a hardware-inspired zero-noise extrapolation method to mitigate quantum gate errors in variational eigensolvers, improving their accuracy by linearly extrapolating to zero error based on circuit error sums.

Contribution

The authors introduce an experimentally feasible zero-noise extrapolation technique that accounts for inhomogeneous gate errors and uses linear fitting to estimate noiseless energies in variational algorithms.

Findings

Energy estimates are approximately linear with circuit error sum.

Linear extrapolation effectively reduces gate errors in variational eigensolvers.

Method demonstrates numerical success and applicability range.

Abstract

Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline in performance due to the presence of stochastic errors and limited coherence time. In this work, we develop a recipe for mitigating quantum gate errors for variational algorithms using zero-noise extrapolation. We introduce an experimentally amenable method to control error strength in the circuit. We utilize the fact that gate errors in a physical quantum device are distributed inhomogeneously over different qubits and qubit pairs. As a result, one can achieve different circuit error sums based on the manner in which abstract qubits in the circuit are mapped to a physical device. We find that the estimated energy in the variational approach is approximately linear with respect to the circuit error sum (CES). Consequently, a linear fit through the energy-CES data, when extrapolated to zero CES, can approximate the energy estimated by a noiseless variational algorithm. We demonstrate this numerically and investigate the applicability range of the technique.