A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control

Abstract

This paper is concerned with variational methods for nonlinear open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. The latter are driven by quantum Wiener processes of the external boson fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations of these energy operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This provides a tool for the infinitesimal perturbation analysis and development of optimality conditions for coherent quantum control problems. We apply the transverse Hamiltonian variational technique to a mean square optimal coherent quantum filtering problem for a measurement-free cascade connection of quantum systems.

12 pages, 1 figure. A brief version of this paper will appear in the proceedings of the IEEE Multi-Conference on Systems and Control, 21-23 September 2015, Sydney, Australia

References in corpus (7)

• Coherent quantum LQG control
• Quantum Feedback Networks: Hamiltonian Formulation
• Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control
• Optimal Quantum Filtering and Quantum Feedback Control
• A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control
• Weyl variations and local sufficiency of linear observers in the mean square optimal coherent quantum filtering problem
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Cited by in corpus (5)

• A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control
• Weyl variations and local sufficiency of linear observers in the mean square optimal coherent quantum filtering problem
• Directly Coupled Observers for Quantum Harmonic Oscillators with Discounted Mean Square Cost Functionals and Penalized Back-action
• A Phase-space Formulation of the Belavkin-Kushner-Stratonovich Filtering Equation for Nonlinear Quantum Stochastic Systems
• Invariant states of linear quantum stochastic systems under Weyl perturbations of the Hamiltonian and coupling operators