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Consensus of quantum networks with continuous-time markovian dynamics

Shi, Guodong; Dong, Daoyi; Petersen, Ian; Johansson , Karl Henrik

Description

In this paper, we investigate the convergence of the state of a quantum network to a consensus (symmetric) state. The state evolution of the quantum network with continuous-time swapping operators can be described by a Lindblad master equation, which also introduces an underlying interaction graph for the network. For a fixed quantum interaction graph, we prove that the state of a quantum network with continuous-time Markovian dynamics converges to a consensus state, with convergence rate given...[Show more]

dc.contributor.authorShi, Guodong
dc.contributor.authorDong, Daoyi
dc.contributor.authorPetersen, Ian
dc.contributor.authorJohansson , Karl Henrik
dc.coverage.spatialShenyang
dc.date.accessioned2015-12-10T21:56:01Z
dc.date.createdJune 29 2014-July 4 2014
dc.identifier.urihttp://hdl.handle.net/1885/39228
dc.description.abstractIn this paper, we investigate the convergence of the state of a quantum network to a consensus (symmetric) state. The state evolution of the quantum network with continuous-time swapping operators can be described by a Lindblad master equation, which also introduces an underlying interaction graph for the network. For a fixed quantum interaction graph, we prove that the state of a quantum network with continuous-time Markovian dynamics converges to a consensus state, with convergence rate given by the smallest nonzero eigenvalue of a matrix serving as the Laplacian of the quantum interaction graph. We show that this convergence rate can be optimized via standard convex programming given a fixed amount of edge weights. For switching quantum interaction graphs, we establish necessary and sufficient conditions for exponential quantum consensus and asymptotic quantum consensus, respectively. The convergence analysis is based on a bridge built between the proposed quantum consensus scheme and classical consensus dynamics, in that quantum consensus of n qubits naturally defines a consensus process on an induced classical graph with 22n nodes. Existing consensus results on classical networks can thus be adopted to establish the quantum consensus convergence.
dc.publisherIEEE
dc.relation.ispartofseries11th World Congress on Intelligent Control and Automation (WCICA) 2014
dc.sourceProceeding of the 11th World Congress on Intelligent Control and Automation
dc.titleConsensus of quantum networks with continuous-time markovian dynamics
dc.typeConference paper
local.description.notesImported from ARIES
dc.date.issued2014
local.identifier.absfor090602 - Control Systems, Robotics and Automation
local.identifier.absfor010203 - Calculus of Variations, Systems Theory and Control Theory
local.identifier.ariespublicationU5431022xPUB173
local.type.statusPublished Version
local.contributor.affiliationShi, Guodong, College of Engineering and Computer Science, ANU
local.contributor.affiliationDong, Daoyi, University of New South Wales
local.contributor.affiliationPetersen, Ian, University of New South Wales, ADFA
local.contributor.affiliationJohansson , Karl Henrik , Access Linnaeus Centre, School of Electrical Engineering
local.description.embargo2037-12-31
local.bibliographicCitation.startpage307
local.bibliographicCitation.lastpage312
local.identifier.doi10.1109/WCICA.2014.7052732
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
local.identifier.absseo970109 - Expanding Knowledge in Engineering
dc.date.updated2015-12-09T07:33:52Z
local.identifier.scopusID2-s2.0-84932165672
CollectionsANU Research Publications

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