Robustness of energy landscape control to dephasing

O’Neil, Sean P.; Langbein, Frank C.; Jonckheere, Edmond; Shermer, Sophie

doi:10.1017/qut.2023.6

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Robustness of energy landscape control to dephasing

Sean P. O’Neil

, Frank C. Langbein

, Edmond Jonckheere, Sophie Shermer

Research Directions: Quantum Technologies, Volume: 1

Swansea University Author: Sophie Shermer

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DOI (Published version): 10.1017/qut.2023.6

Abstract

As shown in previous work, in some cases closed quantum systems exhibit a non-conventional absence of trade-off between performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the in...

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Published in:	Research Directions: Quantum Technologies
ISSN:	2752-9444
Published:	Cambridge University Press (CUP) 2023
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa68718

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last_indexed	2025-03-01T05:37:40Z
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spelling	2025-02-28T15:23:28.9666936 v2 68718 2025-01-20 Robustness of energy landscape control to dephasing 6ebef22eb31eafc75aedcf5bfe487777 0000-0002-5530-7750 Sophie Shermer Sophie Shermer true false 2025-01-20 BGPS As shown in previous work, in some cases closed quantum systems exhibit a non-conventional absence of trade-off between performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the interaction of the system with the environment guides the evolution to a more classically mixed state, it is worth investigating what effect the introduction of dephasing has on the relationship between performance and robustness. In this paper we analyze the robustness of the fidelity error, as measured by the logarithmic sensitivity function, to dephasing processes. We show that introduction of dephasing as a perturbation to the nominal unitary dynamics requires a modification of the log-sensitivity formulation used to measure robustness about an uncertain parameter with nonzero nominal value used in previous work. We consider controllers optimized for a number of target objectives ranging from fidelity under coherent evolution to fidelity under dephasing dynamics to determine the extent to which optimizing for a specific regime has desirable effects in terms of robustness. Our analysis is based on two independent computations of the log-sensitivity: a statistical Monte Carlo approach and an analytic calculation. We show that despite the different log-sensitivity calculations employed in this study, both demonstrate that the log-sensitivity of the fidelity error to dephasing results in a conventional trade-off between performance and robustness. Journal Article Research Directions: Quantum Technologies 1 Cambridge University Press (CUP) 2752-9444 Energy landscape control; spin networks; robust control 2 10 2023 2023-10-02 10.1017/qut.2023.6 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University Another institution paid the OA fee Sean O’Neil acknowledges PhD funding through the US Army Advanced Civil Schooling program. 2025-02-28T15:23:28.9666936 2025-01-20T23:44:29.8133580 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Sean P. O’Neil 0000-0001-6669-4947 1 Frank C. Langbein 0000-0002-3379-0323 2 Edmond Jonckheere 3 Sophie Shermer 0000-0002-5530-7750 4 68718__33716__1531a58b87434f129d7a7af6ebad8f6b.pdf 68718.VoR.pdf 2025-02-28T15:19:42.5452662 Output 802578 application/pdf Version of Record true © The Author(s), 2023. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-ShareAlike licence. true eng http://creativecommons.org/licenses/by-sa/4.0/
title	Robustness of energy landscape control to dephasing
spellingShingle	Robustness of energy landscape control to dephasing Sophie Shermer
title_short	Robustness of energy landscape control to dephasing
title_full	Robustness of energy landscape control to dephasing
title_fullStr	Robustness of energy landscape control to dephasing
title_full_unstemmed	Robustness of energy landscape control to dephasing
title_sort	Robustness of energy landscape control to dephasing
author_id_str_mv	6ebef22eb31eafc75aedcf5bfe487777
author_id_fullname_str_mv	6ebef22eb31eafc75aedcf5bfe487777_***_Sophie Shermer
author	Sophie Shermer
author2	Sean P. O’Neil Frank C. Langbein Edmond Jonckheere Sophie Shermer
format	Journal article
container_title	Research Directions: Quantum Technologies
container_volume	1
publishDate	2023
institution	Swansea University
issn	2752-9444
doi_str_mv	10.1017/qut.2023.6
publisher	Cambridge University Press (CUP)
college_str	Faculty of Science and Engineering
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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
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description	As shown in previous work, in some cases closed quantum systems exhibit a non-conventional absence of trade-off between performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the interaction of the system with the environment guides the evolution to a more classically mixed state, it is worth investigating what effect the introduction of dephasing has on the relationship between performance and robustness. In this paper we analyze the robustness of the fidelity error, as measured by the logarithmic sensitivity function, to dephasing processes. We show that introduction of dephasing as a perturbation to the nominal unitary dynamics requires a modification of the log-sensitivity formulation used to measure robustness about an uncertain parameter with nonzero nominal value used in previous work. We consider controllers optimized for a number of target objectives ranging from fidelity under coherent evolution to fidelity under dephasing dynamics to determine the extent to which optimizing for a specific regime has desirable effects in terms of robustness. Our analysis is based on two independent computations of the log-sensitivity: a statistical Monte Carlo approach and an analytic calculation. We show that despite the different log-sensitivity calculations employed in this study, both demonstrate that the log-sensitivity of the fidelity error to dephasing results in a conventional trade-off between performance and robustness.
published_date	2023-10-02T10:24:25Z
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score	11.055543

Robustness of energy landscape control to dephasing

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