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Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers

E. Jonckheere, S. Schirmer, F. Langbein, Sophie Shermer Orcid Logo

International Journal of Robust and Nonlinear Control, Volume: 28, Issue: 6, Pages: 2383 - 2403

Swansea University Author: Sophie Shermer Orcid Logo

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DOI (Published version): 10.1002/rnc.4022

Abstract

Selective information transfer in spin ring networks by energy landscape shaping control has the property that the error 1−prob, where prob is the transfer success probability, and the sensitivity of the error to spin coupling uncertainties are statistically increasing across a family of controllers...

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Published in: International Journal of Robust and Nonlinear Control
ISSN: 10498923
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa37302
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first_indexed 2017-12-02T05:03:10Z
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spelling 2020-07-14T11:14:00.1663024 v2 37302 2017-12-01 Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers 6ebef22eb31eafc75aedcf5bfe487777 0000-0002-5530-7750 Sophie Shermer Sophie Shermer true false 2017-12-01 SPH Selective information transfer in spin ring networks by energy landscape shaping control has the property that the error 1−prob, where prob is the transfer success probability, and the sensitivity of the error to spin coupling uncertainties are statistically increasing across a family of controllers of increasing error. The need for a statistical Hypothesis Testing of a concordant trend is made necessary by the noisy behavior of the sensitivity versus the error as a consequence of the optimization of the controllers in a challenging error landscape. Here, we examine the concordant trend between the error and another measure of performance—the logarithmic sensitivity—used in robust control to formulate a well known fundamental limitation. Contrary to error versus sensitivity, the error versus logarithmic sensitivity trend is less obvious, because of the amplification of the noise due to the logarithmic normalization. This results in the Kendall τ test for rank correlation between the error and the log sensitivity to be somewhat pessimistic with marginal significance level. Here it is shown that the Jonckheere-Terpstra test, because it tests the Alternative Hypothesis of an ordering of the medians of some groups of log sensitivity data, alleviates this statistical problem. This identifies cases of concordant trend between the error and the logarithmic sensitivity, a highly anti-classical features that goes against the well know sensitivity versus complementary sensitivity limitation. Journal Article International Journal of Robust and Nonlinear Control 28 6 2383 2403 10498923 quantum spin networks, robust control, sensitivity analysis 31 12 2018 2018-12-31 10.1002/rnc.4022 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2020-07-14T11:14:00.1663024 2017-12-01T20:54:34.7686741 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics E. Jonckheere 1 S. Schirmer 2 F. Langbein 3 Sophie Shermer 0000-0002-5530-7750 4 0037302-01122017205507.pdf 1612.02784v2.pdf 2017-12-01T20:55:07.7630000 Output 1024478 application/pdf Accepted Manuscript true 2019-01-12T00:00:00.0000000 true eng
title Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
spellingShingle Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
Sophie Shermer
title_short Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
title_full Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
title_fullStr Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
title_full_unstemmed Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
title_sort Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
author_id_str_mv 6ebef22eb31eafc75aedcf5bfe487777
author_id_fullname_str_mv 6ebef22eb31eafc75aedcf5bfe487777_***_Sophie Shermer
author Sophie Shermer
author2 E. Jonckheere
S. Schirmer
F. Langbein
Sophie Shermer
format Journal article
container_title International Journal of Robust and Nonlinear Control
container_volume 28
container_issue 6
container_start_page 2383
publishDate 2018
institution Swansea University
issn 10498923
doi_str_mv 10.1002/rnc.4022
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 1
active_str 0
description Selective information transfer in spin ring networks by energy landscape shaping control has the property that the error 1−prob, where prob is the transfer success probability, and the sensitivity of the error to spin coupling uncertainties are statistically increasing across a family of controllers of increasing error. The need for a statistical Hypothesis Testing of a concordant trend is made necessary by the noisy behavior of the sensitivity versus the error as a consequence of the optimization of the controllers in a challenging error landscape. Here, we examine the concordant trend between the error and another measure of performance—the logarithmic sensitivity—used in robust control to formulate a well known fundamental limitation. Contrary to error versus sensitivity, the error versus logarithmic sensitivity trend is less obvious, because of the amplification of the noise due to the logarithmic normalization. This results in the Kendall τ test for rank correlation between the error and the log sensitivity to be somewhat pessimistic with marginal significance level. Here it is shown that the Jonckheere-Terpstra test, because it tests the Alternative Hypothesis of an ordering of the medians of some groups of log sensitivity data, alleviates this statistical problem. This identifies cases of concordant trend between the error and the logarithmic sensitivity, a highly anti-classical features that goes against the well know sensitivity versus complementary sensitivity limitation.
published_date 2018-12-31T03:46:57Z
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score 11.014224

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