A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control
Provides a new analytical tool for optimal control of open quantum systems, relevant to quantum engineering and control theory.
The paper develops a transverse Hamiltonian variational technique for analyzing perturbations in Markovian open quantum systems, enabling optimality conditions for coherent quantum control. It applies this to a mean square optimal coherent quantum filtering problem for a cascade of quantum systems.
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.