Volumetric Benchmarking of Error Mitigation with Qermit

Cristina Cirstoiu1,4, Silas Dilkes1,4, Daniel Mills1,4, Seyon Sivarajah1, and Ross Duncan1,2,3

1Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, UK
2Department of Computer and Information Sciences, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK
3Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
4These authors contributed equally:cristina.cirstoiu, silas.dilkes, daniel.mills@quantinuum.com

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Abstract

The detrimental effect of noise accumulates as quantum computers grow in size. In the case where devices are too small or noisy to perform error correction, error mitigation may be used. Error mitigation does not increase the fidelity of quantum states, but instead aims to reduce the approximation error in quantities of concern, such as expectation values of observables. However, it is as yet unclear which circuit types, and devices of which characteristics, benefit most from the use of error mitigation. Here we develop a methodology to assess the performance of quantum error mitigation techniques. Our benchmarks are volumetric in design, and are performed on different superconducting hardware devices. Extensive classical simulations are also used for comparison. We use these benchmarks to identify disconnects between the predicted and practical performance of error mitigation protocols, and to identify the situations in which their use is beneficial. To perform these experiments, and for the benefit of the wider community, we introduce $Qermit$ – an open source python package for quantum error mitigation. Qermit supports a wide range of error mitigation methods, is easily extensible and has a modular graph-based software design that facilitates composition of error mitigation protocols and subroutines.

The collection of computations that existing quantum computers can perform is restricted by errors. When quantum technology sufficiently develops, errors will be suppressed or eradicated, else actively managed and corrected during the computation. Before such technological development occurs, error mitigation may be used to improve the quality of measured quantities extracted from noisy results. Several error mitigation techniques have been proposed, with Zero Noise Extrapolation (ZNE) and Clifford Data Regression (CDR) being two popular examples.

In this work we use ZNE and CDR to mitigate errors when running a selection of classes of quantum computations on a selection of quantum computers. We identify patterns to guide users of quantum computers in selecting an error mitigation strategy to employ when using a particular device and computation. To do this we firstly develop a ‘volumetric’ methodology for assessing the performance of an error mitigation scheme. Secondly, we introduce Qermit; an open source python package for error mitigation with an easily extensible, modular, and composable, graph-based software design.

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[2] Clement Charles, Erik J. Gustafson, Elizabeth Hardt, Florian Herren, Norman Hogan, Henry Lamm, Sara Starecheski, Ruth S. Van de Water, and Michael L. Wagman, "Simulating Z2 lattice gauge theory on a quantum computer", Physical Review E 109 1, 015307 (2024).

[3] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien, "Quantum error mitigation", Reviews of Modern Physics 95 4, 045005 (2023).

[4] Samson Wang, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Lukasz Cincio, and Patrick J. Coles, "Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?", Quantum 8, 1287 (2024).

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