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Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms

Irtaza Khalid, Carrie A. Weidner Orcid Logo, Edmond A. Jonckheere, Sophie Shermer Orcid Logo, Frank C. Langbein Orcid Logo

Physical Review A, Volume: 107, Issue: 3

Swansea University Author: Sophie Shermer Orcid Logo

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DOI (Published version): 10.1103/physreva.107.032606

Abstract

Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIMp) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the pth order Wasserstein distance between the fidelity dis...

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Published in: Physical Review A
ISSN: 2469-9926 2469-9934
Published: American Physical Society (APS) 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa63139
first_indexed 2023-04-13T10:11:22Z
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spelling 2023-05-18T14:35:31.7565375 v2 63139 2023-04-13 Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms 6ebef22eb31eafc75aedcf5bfe487777 0000-0002-5530-7750 Sophie Shermer Sophie Shermer true false 2023-04-13 BGPS Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIMp) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the pth order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The RIMp is the pth root of the pth raw moment of the infidelity distribution. Using a metrization argument, we justify why RIM1 (the average infidelity) is a good practical robustness measure. Based on the RIMp, an algorithmic robustness-infidelity measure (ARIM) is developed to quantify the expected robustness and fidelity of controllers found by a control algorithm. The utility of the RIM and ARIM is demonstrated on energy landscape controllers of spin-12 networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and nonstochastic optimization objectives are considered. Although high fidelity and robustness are often conflicting objectives, some high-fidelity, robust controllers can usually be found, irrespective of the choice of the quantum control algorithm. However, for noisy or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels. Journal Article Physical Review A 107 3 American Physical Society (APS) 2469-9926 2469-9934 Machine learning, Quantum computation, Quantum control, Quantum engineering, Quantum information theory 14 3 2023 2023-03-14 10.1103/physreva.107.032606 http://dx.doi.org/10.1103/physreva.107.032606 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University SU Library paid the OA fee (TA Institutional Deal) 2023-05-18T14:35:31.7565375 2023-04-13T11:06:58.2060392 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Irtaza Khalid 1 Carrie A. Weidner 0000-0001-7776-9836 2 Edmond A. Jonckheere 3 Sophie Shermer 0000-0002-5530-7750 4 Frank C. Langbein 0000-0002-3379-0323 5 63139__27027__0a1fef20189d436f82e79644555e1157.pdf 63139.pdf 2023-04-13T11:10:55.7996705 Output 12586021 application/pdf Version of Record true 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 true eng http://creativecommons.org/licenses/by/4.0/
title Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
spellingShingle Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
Sophie Shermer
title_short Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
title_full Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
title_fullStr Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
title_full_unstemmed Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
title_sort Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms
author_id_str_mv 6ebef22eb31eafc75aedcf5bfe487777
author_id_fullname_str_mv 6ebef22eb31eafc75aedcf5bfe487777_***_Sophie Shermer
author Sophie Shermer
author2 Irtaza Khalid
Carrie A. Weidner
Edmond A. Jonckheere
Sophie Shermer
Frank C. Langbein
format Journal article
container_title Physical Review A
container_volume 107
container_issue 3
publishDate 2023
institution Swansea University
issn 2469-9926
2469-9934
doi_str_mv 10.1103/physreva.107.032606
publisher American Physical Society (APS)
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
url http://dx.doi.org/10.1103/physreva.107.032606
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description Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIMp) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the pth order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The RIMp is the pth root of the pth raw moment of the infidelity distribution. Using a metrization argument, we justify why RIM1 (the average infidelity) is a good practical robustness measure. Based on the RIMp, an algorithmic robustness-infidelity measure (ARIM) is developed to quantify the expected robustness and fidelity of controllers found by a control algorithm. The utility of the RIM and ARIM is demonstrated on energy landscape controllers of spin-12 networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and nonstochastic optimization objectives are considered. Although high fidelity and robustness are often conflicting objectives, some high-fidelity, robust controllers can usually be found, irrespective of the choice of the quantum control algorithm. However, for noisy or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels.
published_date 2023-03-14T20:21:19Z
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