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Consensus of quantum networks with continuous-time markovian dynamics
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2015 (English)In: Proceedings of the World Congress on Intelligent Control and Automation (WCICA), IEEE conference proceedings, 2015, no March, 307-312 p.Conference paper, Published paper (Refereed)
Abstract [en]

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 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.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2015. no March, 307-312 p.
Keyword [en]
Quantum consensus, Quantum control, Quantum network
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-176192DOI: 10.1109/WCICA.2014.7052732Scopus ID: 2-s2.0-84932165672OAI: oai:DiVA.org:kth-176192DiVA: diva2:874912
Conference
2014 11th World Congress on Intelligent Control and Automation, WCICA 2014, 29 June - 4 July 2014
Note

QC 20151130

Available from: 2015-11-30 Created: 2015-11-02 Last updated: 2015-11-30Bibliographically approved

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Johansson, Karl Henrik

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf