Volumetric Benchmarking Of Error Mitigation With Qermit

Cristina Cirstoiu^1,4, Silas Dilkes^1,4, Daniel Mills^1,4, Seyon Sivarajah¹, and Ross Duncan^1,2,3

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, [email protected]

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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.

Featured image: Example comparison of the performance of CDR (left) and ZNE (right) when performed on a real device. Colours from blue to red indicate worsening performance, with red indicating no improvement from using error mitigation over an experiment without error mitigation. Axes give circuit size, outer squares give median performance, and inner squares give worst case performance.

Popular summary

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.

► BibTeX data

@article{Cirstoiu2023volumetric, doi = {10.22331/q-2023-07-13-1059}, url = {https://doi.org/10.22331/q-2023-07-13-1059}, title = {Volumetric {B}enchmarking of {E}rror {M}itigation with {Q}ermit}, author = {Cirstoiu, Cristina and Dilkes, Silas and Mills, Daniel and Sivarajah, Seyon and Duncan, Ross}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1059}, month = jul, year = {2023}<br /> }

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Cited by

[1] He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long, “Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation”, Science China Physics, Mechanics, and Astronomy 66 5, 250302 (2023).

[2] Abdullah Ash Saki, Amara Katabarwa, Salonik Resch, and George Umbrarescu, “Hypothesis Testing for Error Mitigation: How to Evaluate Error Mitigation”, arXiv:2301.02690, (2023).

[3] 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 $mathbb{Z}_2$ lattice gauge theory on a quantum computer”, arXiv:2305.02361, (2023).

[4] Tom Weber, Kerstin Borras, Karl Jansen, Dirk Krücker, and Matthias Riebisch, “Volumetric Benchmarking of Quantum Computing Noise Models”, arXiv:2306.08427, (2023).

[5] Alejandro Sopena, Max Hunter Gordon, Diego García-Martín, Germán Sierra, and Esperanza López, “Algebraic Bethe Circuits”, Quantum 6, 796 (2022).

[6] Enrico Fontana, Ivan Rungger, Ross Duncan, and Cristina Cîrstoiu, “Spectral analysis for noise diagnostics and filter-based digital error mitigation”, arXiv:2206.08811, (2022).

[7] Olivia Di Matteo and R. M. Woloshyn, “Quantum computing fidelity susceptibility using automatic differentiation”, Physical Review A 106 5, 052429 (2022).

[8] Chris N. Self, Sofyan Iblisdir, Gavin K. Brennen, and Konstantinos Meichanetzidis, “Estimating the Jones polynomial for Ising anyons on noisy quantum computers”, arXiv:2210.11127, (2022).

[9] Seyon Sivarajah, Lukas Heidemann, Alan Lawrence, and Ross Duncan, “Tierkreis: A Dataflow Framework for Hybrid Quantum-Classical Computing”, arXiv:2211.02350, (2022).

[10] Piotr Czarnik, Michael McKerns, Andrew T. Sornborger, and Lukasz Cincio, “Robust design under uncertainty in quantum error mitigation”, arXiv:2307.05302, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-07-13 15:08:14). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-07-13 15:08:12: Could not fetch cited-by data for 10.22331/q-2023-07-13-1059 from Crossref. This is normal if the DOI was registered recently.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-07-13-1059/

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Volumetric Benchmarking of Error Mitigation with Qermit

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