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The accuracy vs. sampling overhead trade-off in quantum error mitigation using Monte Carlo-based channel inversion

The accuracy vs. sampling overhead trade-off in quantum error mitigation using Monte Carlo-based channel inversion
The accuracy vs. sampling overhead trade-off in quantum error mitigation using Monte Carlo-based channel inversion
Quantum error mitigation (QEM) is a class of promising techniques for reducing the computational error of variational quantum algorithms. In general, the computational error reduction comes at the cost of a sampling overhead due to the variance-boosting effect caused by the channel inversion operation, which ultimately limits the applicability of QEM. Existing sampling overhead analysis of QEM typically assumes exact channel inversion, which is unrealistic in practical scenarios. In this treatise, we consider a practical channel inversion strategy based on Monte Carlo sampling, which introduces additional computational error that in turn may be eliminated at the cost of an extra sampling overhead. In particular, we show that when the computational error is small compared to the dynamic range of the error-free results, it scales with the square root of the number of gates. By contrast, the error exhibits a linear scaling with the number of gates in the absence of QEM under the same assumptions. Hence, the error scaling of QEM remains to be preferable even without the extra sampling overhead. Our analytical results are accompanied by numerical examples.
Computers, Logic gates, Monte Carlo methods, Quantum circuit, Quantum computing, Qubit, Task analysis
0090-6778
1943-1956
Xiong, Yifeng
f93bfe9b-7a6d-47e8-a0a8-7f4f6632ab21
Ng, Soon Xin
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Xiong, Yifeng
f93bfe9b-7a6d-47e8-a0a8-7f4f6632ab21
Ng, Soon Xin
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Xiong, Yifeng, Ng, Soon Xin and Hanzo, Lajos (2022) The accuracy vs. sampling overhead trade-off in quantum error mitigation using Monte Carlo-based channel inversion. IEEE Transactions on Communications, 70 (3), 1943-1956. (doi:10.1109/TCOMM.2022.3144469).

Record type: Article

Abstract

Quantum error mitigation (QEM) is a class of promising techniques for reducing the computational error of variational quantum algorithms. In general, the computational error reduction comes at the cost of a sampling overhead due to the variance-boosting effect caused by the channel inversion operation, which ultimately limits the applicability of QEM. Existing sampling overhead analysis of QEM typically assumes exact channel inversion, which is unrealistic in practical scenarios. In this treatise, we consider a practical channel inversion strategy based on Monte Carlo sampling, which introduces additional computational error that in turn may be eliminated at the cost of an extra sampling overhead. In particular, we show that when the computational error is small compared to the dynamic range of the error-free results, it scales with the square root of the number of gates. By contrast, the error exhibits a linear scaling with the number of gates in the absence of QEM under the same assumptions. Hence, the error scaling of QEM remains to be preferable even without the extra sampling overhead. Our analytical results are accompanied by numerical examples.

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Accepted/In Press date: 15 January 2022
e-pub ahead of print date: 20 January 2022
Additional Information: Publisher Copyright: IEEE Copyright: Copyright 2022 Elsevier B.V., All rights reserved.
Keywords: Computers, Logic gates, Monte Carlo methods, Quantum circuit, Quantum computing, Qubit, Task analysis

Identifiers

Local EPrints ID: 454206
URI: http://eprints.soton.ac.uk/id/eprint/454206
ISSN: 0090-6778
PURE UUID: b46c944c-e1b3-467d-83e3-f2ee78f1ec56
ORCID for Yifeng Xiong: ORCID iD orcid.org/0000-0002-4290-7116
ORCID for Soon Xin Ng: ORCID iD orcid.org/0000-0002-0930-7194
ORCID for Lajos Hanzo: ORCID iD orcid.org/0000-0002-2636-5214

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Date deposited: 02 Feb 2022 17:47
Last modified: 28 Apr 2022 02:25

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Contributors

Author: Yifeng Xiong ORCID iD
Author: Soon Xin Ng ORCID iD
Author: Lajos Hanzo ORCID iD

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