Synthesis of linear quantum stochastic systems via quantum feedback networks

Hendra I. Nurdin

    Research output: Contribution to journalArticlepeer-review

    40 Citations (Scopus)


    Recent theoretical and experimental investigations of coherent feedback quantum control, the feedback control of a quantum system with another quantum system, has raised the important problem of how to synthesize a class of quantum systems, called the class of linear quantum stochastic systems, from basic quantum optical components and devices in a systematic way. The synthesis theory sought in this case can be naturally viewed as a quantum analogue of linear electrical network synthesis theory and as such has potential for applications beyond the realization of coherent quantum feedback controllers. In earlier work, Nurdin et al. have established that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators, together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental perspective and based on current methods and technologies, direct interaction Hamiltonians are challenging to implement for systems with more than just a few degrees of freedom. In order to facilitate more tractable physical realizations of these systems, this technical note develops a new synthesis algorithm for linear quantum stochastic systems that relies solely on field-mediated interactions, including in implementation of the direct interaction Hamiltonian. Explicit synthesis examples are provided to illustrate the realization of two degrees of freedom linear quantum stochastic systems using the new algorithm.

    Original languageEnglish
    Article number5404766
    Pages (from-to)1008-1013
    Number of pages6
    JournalIEEE Transactions on Automatic Control
    Issue number4
    Publication statusPublished - Apr 2010


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