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Measurement-induced Boolean dynamics and controllability for closed quantum networks

Qi, Hongsheng; Mu, Biqiang; Petersen, Ian; Shi, Guodong

Description

In this paper, we study dynamical quantum networks which evolve according to Schrödinger equations but subject to sequential local or global quantum measurements. A network of qubits forms a composite quantum system whose state undergoes unitary evolution in between periodic measurements, leading to hybrid quantum dynamics with random jumps at discrete time instances along a continuous orbit. The measurements either act on the entire network of qubits, or only a subset of qubits. First of...[Show more]

dc.contributor.authorQi, Hongsheng
dc.contributor.authorMu, Biqiang
dc.contributor.authorPetersen, Ian
dc.contributor.authorShi, Guodong
dc.date.accessioned2023-09-05T00:10:08Z
dc.identifier.issn0005-1098
dc.identifier.urihttp://hdl.handle.net/1885/298212
dc.description.abstractIn this paper, we study dynamical quantum networks which evolve according to Schrödinger equations but subject to sequential local or global quantum measurements. A network of qubits forms a composite quantum system whose state undergoes unitary evolution in between periodic measurements, leading to hybrid quantum dynamics with random jumps at discrete time instances along a continuous orbit. The measurements either act on the entire network of qubits, or only a subset of qubits. First of all, we reveal that this type of hybrid quantum dynamics induces probabilistic Boolean recursions representing the measurement outcomes. With global measurements, it is shown that such resulting Boolean recursions define Markov chains whose state-transitions are fully determined by the network Hamiltonian and the measurement observables. Particularly, we establish an explicit and algebraic representation of the underlying recursive random mapping driving such induced Markov chains. Next, with local measurements, the resulting probabilistic Boolean dynamics is shown to be no longer Markovian. The state transition probability at any given time becomes dependent on the entire history of the sample path, for which we establish a recursive way of computing such non-Markovian probability transitions. Finally, we adopt the classical bilinear control model for the continuous Schrödinger evolution, and show how the measurements affect the controllability of the quantum networks.
dc.description.sponsorshipThis research was supported in part by the National Key R&D Program of China under Grant 2018YFA0703800, the National Natural Science Foundation of China under Grants 61873262 and 61733018, and the Australian Research Council under Grants DP180101805 and DP190103615. The material in this paper was not presented at any conference
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherElsevier Ltd
dc.rights© 2020 Elsevier Ltd.
dc.sourceAutomatica
dc.subjectQuantum networks
dc.subjectQuantum measurements
dc.subjectBilinear systems
dc.subjectBoolean networks
dc.titleMeasurement-induced Boolean dynamics and controllability for closed quantum networks
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume114
dc.date.issued2020
local.identifier.absfor400705 - Control engineering
local.identifier.ariespublicationu6269649xPUB485
local.publisher.urlhttps://www.elsevier.com/en-au
local.type.statusAccepted Version
local.contributor.affiliationQi, Hongsheng, Chinese Academy of Sciences
local.contributor.affiliationMu, Biqiang, Chinese Academy of Sciences
local.contributor.affiliationPetersen, Ian, College of Engineering and Computer Science, ANU
local.contributor.affiliationShi, Guodong, The University of Sydney
dc.relationhttp://purl.org/au-research/grants/arc/DP180101805
dc.relationhttp://purl.org/au-research/grants/arc/DP190103615
local.bibliographicCitation.startpage1
local.bibliographicCitation.lastpage11
local.identifier.doi10.1016/j.automatica.2020.108816
local.identifier.absseo280110 - Expanding knowledge in engineering
dc.date.updated2022-07-24T08:22:07Z
local.identifier.scopusID2-s2.0-85077952964
local.identifier.thomsonIDWOS:000519656500009
dc.provenancehttps://v2.sherpa.ac.uk/id/publication/4278..."The Accepted Version can be archived in an Institutional Repository. 24 Months embargo. CC BY-NC-ND ." from SHERPA/RoMEO site (as at 6/09/2023).
dc.rights.licenseCC BY-NC-ND
dc.rights.licensehttp://creativecommons.org/licenses/by-nc-nd/4.0/
CollectionsANU Research Publications

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