Low-cost error mitigation by symmetry verification

TL;DR

This paper explores low-cost error mitigation techniques using symmetry verification in quantum computing, introducing protocols and methods to measure and utilize symmetries for improved accuracy on near-term devices.

Contribution

It presents new protocols for symmetry measurement and methods to incorporate symmetries into quantum algorithms, enhancing error mitigation without additional quantum resources.

Findings

Up to tenfold error reduction in hydrogen molecule simulations

Protocols effective for both global and local symmetries

Demonstrated on classical simulators with promising results

Abstract

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a zero-cost post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost their mitigation against different error channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground state dissociation curve.