Interpolation of positive matrices by quantum-inspired optimal control

Jiang, C; Pan, Y; Yang, Y; Dong, D

Interpolation of positive matrices by quantum-inspired optimal control

Jiang, C Pan, Y Yang, Y Dong, D

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Publisher:: WILEY
Publication Type:: Journal Article
Citation:: IET Control Theory and Applications, 2024, 18, (7), pp. 877-886
Issue Date:: 2024-04-01

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Field	Value	Language
dc.contributor.author	Jiang, C
dc.contributor.author	Pan, Y
dc.contributor.author	Yang, Y
dc.contributor.author	Dong, D https://orcid.org/0000-0002-7425-3559
dc.date.accessioned	2025-04-03T06:17:19Z
dc.date.available	2025-04-03T06:17:19Z
dc.date.issued	2024-04-01
dc.identifier.citation	IET Control Theory and Applications, 2024, 18, (7), pp. 877-886
dc.identifier.issn	1751-8644
dc.identifier.issn	1751-8652
dc.identifier.uri	http://hdl.handle.net/10453/186563
dc.description.abstract	Interpolation of probability distributions can be formulated as an optimal transport problem. Positive matrix, which can be viewed as the generalization of probability distribution to higher dimension, is used in quantum theory to describe the state of a quantum system. Here, a quantum-inspired method for the interpolation of positive matrices is proposed. Particularly, this method employs the quantum state purification of the positive matrices in an extended space. Since pure state controllability can be easily achieved using open-loop coherent control, the continuous interpolation of positive matrices is given as a completely positive map induced by simulating the optimal control for pure state transfer. The quantum-inspired interpolation is shape-preserving with applications to tensor field processing.
dc.language	English
dc.publisher	WILEY
dc.relation.ispartof	IET Control Theory and Applications
dc.relation.isbasedon	10.1049/cth2.12625
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0102 Applied Mathematics, 0906 Electrical and Electronic Engineering, 0913 Mechanical Engineering
dc.subject.classification	Industrial Engineering & Automation
dc.subject.classification	4007 Control engineering, mechatronics and robotics
dc.subject.classification	4008 Electrical engineering
dc.subject.classification	4901 Applied mathematics
dc.title	Interpolation of positive matrices by quantum-inspired optimal control
dc.type	Journal Article
utslib.citation.volume	18
utslib.for	0102 Applied Mathematics
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	0913 Mechanical Engineering
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/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	open_access	*
dc.rights.license	This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/
dc.date.updated	2025-04-03T06:17:18Z
pubs.issue	7
pubs.publication-status	Published
pubs.volume	18
utslib.citation.issue	7

Abstract:

Interpolation of probability distributions can be formulated as an optimal transport problem. Positive matrix, which can be viewed as the generalization of probability distribution to higher dimension, is used in quantum theory to describe the state of a quantum system. Here, a quantum-inspired method for the interpolation of positive matrices is proposed. Particularly, this method employs the quantum state purification of the positive matrices in an extended space. Since pure state controllability can be easily achieved using open-loop coherent control, the continuous interpolation of positive matrices is given as a completely positive map induced by simulating the optimal control for pure state transfer. The quantum-inspired interpolation is shape-preserving with applications to tensor field processing.

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http://hdl.handle.net/10453/186563