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  • Open Access

Practical Quantum Error Mitigation for Near-Future Applications

Suguru Endo1, Simon C. Benjamin1, and Ying Li2,1,*

  • 1Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
  • 2Graduate School of China Academy of Engineering Physics, Beijing 100193, China

  • *ying.li.phys@gmail.com
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Phys. Rev. X 8, 031027 – Published 26 July, 2018

DOI: https://doi.org/10.1103/PhysRevX.8.031027

Abstract

It is vital to minimize 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 [Y. Li and S. C. Benjamin, Phys. Rev. X 7, 021050 (2017); K. Temme et al., Phys. Rev. Lett. 119, 180509 (2017)] and quasiprobability decomposition [K. Temme et al., Phys. Rev. Lett. 119, 180509 (2017)]. 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 localized 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 optimized methods dramatically reduce the circuit’s output error without increasing the qubit count.

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Popular Summary

The first generation of quantum computers with more than 50 quantum bits, or qubits, is expected to emerge in the next 12 months. That is large enough to go beyond the predictive power of conventional supercomputers. However, these early quantum computers will also be prone to errors, potentially preventing them from being useful. We show that one recently proposed solution—writing quantum software in such a way that errors do as little harm as possible—can work even if we have imperfect knowledge of the nature of the errors, as will certainly be the case in reality.

The goal of “quantum error mitigation” is to estimate the value that some observable would take in a circuit free from errors. Focusing on two recent proposals for practically accomplishing this goal, we account for inevitable imperfections in the knowledge of the underlying error model. We describe a protocol for systematically measuring the effect of errors so as to design efficient circuits. We prove that quantum error mitigation can work for quantum computers with up to 20 qubits, and we estimate that it will still work for computers with more than 50 qubits.

This is good news. While quantum computers might start to be useful beyond 50 qubits, the lack of any error mitigation would be a showstopper. Also, this technique is “free,” in the sense that it does not need any extra qubits or other technological features to operate—it is just a smarter way to structure the quantum software.

Article Text

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Outline

Information

Phys. Rev. X 8, 031027– Published 26 July, 2018
  • Received 24 January 2018
  • Revised 15 May 2018
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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