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Robustness of dynamic quantum control: Differential sensitivity bounds

S. P. O'Neil Orcid Logo, C. A. Weidner Orcid Logo, E. A. Jonckheere Orcid Logo, F. C. Langbein Orcid Logo, Sophie Shermer Orcid Logo

AVS Quantum Science, Volume: 6, Issue: 3

Swansea University Author: Sophie Shermer Orcid Logo

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DOI (Published version): 10.1116/5.0196110

Abstract

Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of...

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Published in: AVS Quantum Science
ISSN: 2639-0213
Published: American Vacuum Society 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa68713
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While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper, a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error can be reliably computed. 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Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.</abstract><type>Journal Article</type><journal>AVS Quantum Science</journal><volume>6</volume><journalNumber>3</journalNumber><paginationStart/><paginationEnd/><publisher>American Vacuum Society</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic>2639-0213</issnElectronic><keywords/><publishedDay>1</publishedDay><publishedMonth>9</publishedMonth><publishedYear>2024</publishedYear><publishedDate>2024-09-01</publishedDate><doi>10.1116/5.0196110</doi><url/><notes/><college>COLLEGE NANME</college><department>Biosciences Geography and Physics School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>BGPS</DepartmentCode><institution>Swansea University</institution><apcterm>Not Required</apcterm><funders>Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. 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spelling 2025-02-28T13:24:21.6114251 v2 68713 2025-01-20 Robustness of dynamic quantum control: Differential sensitivity bounds 6ebef22eb31eafc75aedcf5bfe487777 0000-0002-5530-7750 Sophie Shermer Sophie Shermer true false 2025-01-20 BGPS Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper, a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties. Journal Article AVS Quantum Science 6 3 American Vacuum Society 2639-0213 1 9 2024 2024-09-01 10.1116/5.0196110 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University Not Required Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper, a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties. 2025-02-28T13:24:21.6114251 2025-01-20T23:15:18.0180306 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics S. P. O'Neil 0000-0001-6669-4947 1 C. A. Weidner 0000-0001-7776-9836 2 E. A. Jonckheere 0000-0002-7205-4273 3 F. C. Langbein 0000-0002-3379-0323 4 Sophie Shermer 0000-0002-5530-7750 5 68713__33712__c387187af4614789ac9af3184514e42b.pdf 68713.VoR.pdf 2025-02-28T13:21:19.8792640 Output 3244117 application/pdf Version of Record true Copyright: 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license. true eng https://creativecommons.org/licenses/by/4.0/
title Robustness of dynamic quantum control: Differential sensitivity bounds
spellingShingle Robustness of dynamic quantum control: Differential sensitivity bounds
Sophie Shermer
title_short Robustness of dynamic quantum control: Differential sensitivity bounds
title_full Robustness of dynamic quantum control: Differential sensitivity bounds
title_fullStr Robustness of dynamic quantum control: Differential sensitivity bounds
title_full_unstemmed Robustness of dynamic quantum control: Differential sensitivity bounds
title_sort Robustness of dynamic quantum control: Differential sensitivity bounds
author_id_str_mv 6ebef22eb31eafc75aedcf5bfe487777
author_id_fullname_str_mv 6ebef22eb31eafc75aedcf5bfe487777_***_Sophie Shermer
author Sophie Shermer
author2 S. P. O'Neil
C. A. Weidner
E. A. Jonckheere
F. C. Langbein
Sophie Shermer
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container_title AVS Quantum Science
container_volume 6
container_issue 3
publishDate 2024
institution Swansea University
issn 2639-0213
doi_str_mv 10.1116/5.0196110
publisher American Vacuum Society
college_str Faculty of Science and Engineering
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
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department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
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description Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper, a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.
published_date 2024-09-01T05:45:20Z
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