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Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations

Sophie Shermer Orcid Logo, Carrie Weidner Orcid Logo, Edmond Jonckheere Orcid Logo, Frank Langbein Orcid Logo

arXiv

Swansea University Author: Sophie Shermer Orcid Logo

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DOI (Published version): 10.48550/arXiv.2207.12385

Abstract

Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfi...

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Published in: arXiv
Published: To appear in IEEE CDC 2022 2022
URI: https://cronfa.swan.ac.uk/Record/cronfa61773
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first_indexed 2022-11-03T18:13:39Z
last_indexed 2023-01-13T19:22:45Z
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spelling 2022-11-29T12:06:55.0213460 v2 61773 2022-11-03 Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations 6ebef22eb31eafc75aedcf5bfe487777 0000-0002-5530-7750 Sophie Shermer Sophie Shermer true false 2022-11-03 SPH Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to non-unitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control. Journal Article arXiv To appear in IEEE CDC 2022 25 7 2022 2022-07-25 10.48550/arXiv.2207.12385 Preprint article before certification by peer review. https://arxiv.org/abs/2207.12385 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2022-11-29T12:06:55.0213460 2022-11-03T17:42:26.4385681 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Sophie Shermer 0000-0002-5530-7750 1 Carrie Weidner 0000-0001-7776-9836 2 Edmond Jonckheere 0000-0002-7205-4273 3 Frank Langbein 0000-0002-3379-0323 4
title Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
spellingShingle Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
Sophie Shermer
title_short Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
title_full Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
title_fullStr Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
title_full_unstemmed Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
title_sort Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations
author_id_str_mv 6ebef22eb31eafc75aedcf5bfe487777
author_id_fullname_str_mv 6ebef22eb31eafc75aedcf5bfe487777_***_Sophie Shermer
author Sophie Shermer
author2 Sophie Shermer
Carrie Weidner
Edmond Jonckheere
Frank Langbein
format Journal article
container_title arXiv
publishDate 2022
institution Swansea University
doi_str_mv 10.48550/arXiv.2207.12385
publisher To appear in IEEE CDC 2022
college_str Faculty of Science and Engineering
hierarchytype
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
document_store_str 0
active_str 0
description Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to non-unitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control.
published_date 2022-07-25T04:20:51Z
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score 11.035634

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