Practical Quantum Error Mitigation for Near-Future Applications

TL;DR

This paper presents practical quantum error mitigation techniques that effectively reduce errors in near-term quantum devices by accounting for imperfect error models and optimizing error correction circuits.

Contribution

It introduces a systematic protocol for measuring error effects, optimizes error mitigation circuits, and compares extrapolation and quasi-probability methods through simulations.

Findings

Localised Markovian errors can be fully mitigated with specific gate replacements.

The exponential extrapolation method enhances error reduction.

Optimized techniques significantly lower output errors without extra qubits or time.

Abstract

It is vital to minimise the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely error extrapolation [Li2017,Temme2017] and quasi-probability decomposition [Temme2017]. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist's knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effect of localised Markovian errors can be fully eliminated by inserting or replacing some gates with certain single-qubit Clifford gates and measurements. Finally, having introduced an exponential variant of the extrapolation method we contrast the QEM techniques using exact numerical simulation of up to 19 qubits in the context of a `SWAP test' circuit. Our optimised methods dramatically reduce the circuit's output error without increasing the qubit count or time requirements.