Network Synthesis of Linear Dynamical Quantum Stochastic Systems

Abstract

The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory will enable the systematic realization of coherent/fully quantum linear stochastic controllers for quantum control, amongst other potential applications. We show how general linear dynamical quantum stochastic systems can be constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, discuss how such a network of oscillators can be approximately synthesized or implemented in a systematic way from some linear and non-linear quantum optical elements. An example is also provided to illustrate the theory.

Revised and corrected version, published in SIAM Journal on Control and Optimization, 2009

References in corpus (7)

• Coherent quantum LQG control
• Coherent-feedback quantum control with a dynamic compensator
• Quantum Feedback Networks: Hamiltonian Formulation
• Robust quantum parameter estimation: coherent magnetometry with feedback
• Optimal Quantum Filtering and Quantum Feedback Control
• Synthesis of linear quantum stochastic systems via quantum feedback networks
• Quantum teleportation between nanomechanical modes

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