Robust Mean Square Stability of Open Quantum Stochastic Systems with Hamiltonian Perturbations in a Weyl Quantization Form

TL;DR

This paper establishes conditions under which open quantum stochastic systems with Hamiltonian perturbations in Weyl form maintain robust mean square stability, extending stability analysis to uncertain quantum Hamiltonians.

Contribution

It introduces a method to ensure stability of quantum systems with Hamiltonian uncertainties expressed in Weyl quantization form, broadening robustness analysis in quantum control.

Findings

Derived sufficient stability conditions for perturbed quantum systems.

Provided examples with trigonometric polynomial Hamiltonian perturbations.

Extended classical robustness concepts to quantum stochastic systems.

Abstract

This paper is concerned with open quantum systems whose dynamic variables satisfy canonical commutation relations and are governed by quantum stochastic differential equations. The latter are driven by quantum Wiener processes which represent external boson fields. The system-field coupling operators are linear functions of the system variables. The Hamiltonian consists of a nominal quadratic function of the system variables and an uncertain perturbation which is represented in a Weyl quantization form. Assuming that the nominal linear quantum system is stable, we develop sufficient conditions on the perturbation of the Hamiltonian which guarantee robust mean square stability of the perturbed system. Examples are given to illustrate these results for a class of Hamiltonian perturbations in the form of trigonometric polynomials of the system variables.