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

TL;DR

This paper introduces a transverse Hamiltonian variational method for analyzing and optimizing open quantum stochastic systems, enabling better understanding and control of quantum systems driven by stochastic differential equations.

Contribution

It develops a novel transverse Hamiltonian approach for perturbation analysis and optimality conditions in coherent quantum control, applied to quantum filtering problems.

Findings

Provides a new variational technique for quantum system analysis

Enables derivation of optimality conditions for quantum control

Demonstrates application to quantum filtering in cascade systems

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.