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Scalable Mitigation of Measurement Errors on Quantum Computers

Paul D. Nation*, Hwajung Kang, Neereja Sundaresan, and Jay M. Gambetta

  • IBM Quantum, Yorktown Heights, New York 10598, USA

  • *paul.nation@ibm.com
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PRX Quantum 2, 040326 – Published 8 November, 2021

DOI: https://doi.org/10.1103/PRXQuantum.2.040326

Abstract

We present a method for mitigating measurement errors on quantum computing platforms that does not form the full assignment matrix, or its inverse, and works in a subspace defined by the noisy input bit strings. This method accommodates both uncorrelated and correlated errors and allows for the computation of accurate error bounds. Additionally, we detail a matrix-free preconditioned iterative-solution method that converges in O(1) steps that is performant and uses orders of magnitude less memory than direct factorization. We demonstrate the validity of our method and mitigate errors in a few seconds on numbers of qubits that would otherwise be impractical.

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The rapid development and deployment of quantum computing systems has brought us ever closer to the goal of reaching quantum advantage; the point at which executing one of more tasks on a quantum computer provides tangible benefits over classical computation methods. However, at the same time, noise and errors in near-term quantum devices greatly limit their full potential. As such, researchers have developed several mitigation strategies to approximately cancel quantum gate and measurement errors and boost the fidelity of experiments executed on these systems. In many quantum computing architectures, measurement errors play an outsized role and their mitigation is essential to getting accurate results for many near-term applications and algorithms. To date, the mitigation of measurement errors has been greatly limited by the exponential scaling of current techniques with the number of measured qubits. This bottleneck limits the use of present-day measurement-mitigation strategies to just a handful of qubits and prevents them from being used at scales needed for quantum advantage and beyond.

In this work, we present a scalable way of mitigating quantum measurement errors that allows for the mitigation of errors on numbers of qubits that would otherwise be out of reach for even the largest of supercomputers using previous methods. To achieve this, we put forth a truncation scheme that reduces the exponential overhead down to a scaling that depends on the number of observed bit strings and can be readily solved using standard computational methods. Our method works for both uncorrelated and correlated errors and yields accurate error bounds. We then take this reduction a step further and create a matrix-free method iterative method that mitigates measurement errors and is both performant and memory efficient. The validity of the truncation technique is experimentally verified and we perform mitigation experiments out to numbers of qubits that are otherwise impractical to solve.

Our techniques remove one of the long-standing roadblocks to performing high-fidelity experiments on many quantum computing platforms and open the door to mitigating measurement errors at scales amenable to demonstrations of quantum advantage.

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PRX Quantum 2, 040326– Published 8 November, 2021
  • Received 6 September 2021
  • Accepted 8 October 2021
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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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