Quantum network reduced-state synchronization part II-the missing symmetry and switching interactions

Guodong Shi, Shuangshuang Fu, Ian R. Petersen

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    5 Citations (Scopus)


    We consider reduced-state synchronization of qubit networks with the aim of driving the qubits' reduced states to a common trajectory. The evolution of the quantum network's state is described by a master equation, where the network Hamiltonian is either a direct sum or a tensor product of identical qubit Hamiltonians, and the coupling terms are given by a set of permutation operators over the network. The permutations introduce naturally quantum directed interactions. Part I of the paper establishes synchronization conditions for fixed quantum interactions. In this part of the paper, we further investigate the missing symmetry in the reduced-state synchronization from a graphical point of view. The information-flow hierarchy in quantum permutation operators is characterized by different layers of information-induced graphs, based on which a clear bridge between quantum and classical consensus dynamics is built. We show that the quantum synchronization equation is by nature equivalent to a cut-balanced consensus process. Then a necessary and sufficient condition is obtained for reaching quantum reduced-state synchronization in light of recent work by Hendrickx and Tsitsiklis [19].

    Original languageEnglish
    Title of host publicationACC 2015 - 2015 American Control Conference
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Number of pages6
    ISBN (Electronic)9781479986842
    Publication statusPublished - 28 Jul 2015
    Event2015 American Control Conference, ACC 2015 - Chicago, United States
    Duration: 1 Jul 20153 Jul 2015

    Publication series

    NameProceedings of the American Control Conference
    ISSN (Print)0743-1619


    Conference2015 American Control Conference, ACC 2015
    Country/TerritoryUnited States


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