Quantum geometric machine learning for quantum circuits and control

Perrier, E; Tao, D; Ferrie, C

Quantum geometric machine learning for quantum circuits and control

Perrier, E Tao, D

Ferrie, C

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Publisher:: IOP Publishing
Publication Type:: Journal Article
Citation:: New Journal of Physics, 2020, 22, (10), pp. 103056-103056
Issue Date:: 2020-10-01

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Field	Value	Language
dc.contributor.author	Perrier, E
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449
dc.contributor.author	Ferrie, C https://orcid.org/0000-0003-2736-9943
dc.date.accessioned	2021-03-29T19:31:30Z
dc.date.available	2021-03-29T19:31:30Z
dc.date.issued	2020-10-01
dc.identifier.citation	New Journal of Physics, 2020, 22, (10), pp. 103056-103056
dc.identifier.issn	1367-2630
dc.identifier.issn	1367-2630
dc.identifier.uri	http://hdl.handle.net/10453/147628
dc.description.abstract	© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches for solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with whitebox models (which encode prior domain knowledge of quantum mechanics), as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
dc.language	en
dc.publisher	IOP Publishing
dc.relation.ispartof	New Journal of Physics
dc.relation.isbasedon	http://dx.doi.org/10.1088/1367-2630/abbf6b
dc.rights	This is an author-created, un-copyedited version of an article accepted for publication in New Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at http://dx.doi.org/10.1088/1367-2630/abbf6b.	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	02 Physical Sciences
dc.subject.classification	Fluids & Plasmas
dc.title	Quantum geometric machine learning for quantum circuits and control
dc.type	Journal Article
utslib.citation.volume	22
utslib.for	020603 Quantum Information, Computation and Communication
utslib.for	02 Physical Sciences
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	open_access	*
dc.date.updated	2021-03-29T19:31:27Z
pubs.issue	10
pubs.publication-status	Published
pubs.volume	22
utslib.citation.issue	10

Abstract:

© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches for solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with whitebox models (which encode prior domain knowledge of quantum mechanics), as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.

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http://hdl.handle.net/10453/147628