Robust stability of uncertain quantum systems

Abstract

Abstract-This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the system Hamiltonian. Then, the special case of a nominal linear quantum system is considered with either quadratic or nonquadratic perturbations to the system Hamiltonian. In this case, robust stability conditions are given in terms of strict bounded real conditions.

Robust mean square stability of open quantum stochastic systems with Hamiltonian perturbations in a Weyl quantization form

“…MEAN SQUARE STABILITY The following lemma provides sufficient conditions of mean square stability [15], [16] of the perturbed quantum system (6).…”

“…The robustness of various classes of perturbed open quantum systems, modelled by QSDEs, has been addressed in the literature using dissipativity theory and different notions of stability (see for example [15], [16], [20], [21]). In particular, robust mean square stability with respect to a class of perturbations of Hamiltonians has been studied in [15] and its applications have been presented in [17], [18].…”

“…In particular, robust mean square stability with respect to a class of perturbations of Hamiltonians has been studied in [15] and its applications have been presented in [17], [18]. In these papers, the classical and quantum models of the perturbed Hamiltonian are related by using power series of quantum variables in combination with Wick's quantization [1, pp.…”

“…In this framework, which follows the Heisenberg picture of quantum dynamics, a quantum noise is introduced in order to represent the surroundings as a heat bath of external fields acting on a boson Fock space [14]. The QSDE approach to open quantum systems is employed by the quantum dissipative systems theory [8] which addresses robust stability issues.The robustness of various classes of perturbed open quantum systems, modelled by QSDEs, has been addressed in the literature using dissipativity theory and different notions of stability (see for example [15], [16], [20], [21]). In particular, robust mean square stability with respect to a class of perturbations of Hamiltonians has been studied in [15] and its applications have been presented in [17], [18].…”

A Popov approach to performance analysis and coherent guaranteed cost control for uncertain quantum systems

“…In this approach, a controller Hamiltonian is added to the given system and the physical realizability condition does not need to be considered, as the controller system defined by (S, L, H) automatically represents a physically realizable quantum system. This (S, L, H) framework has been considered in many recent papers; e.g., [4]- [12]. In this paper, we designed a coherent quantum controller using the framework of triples (S, L, H).…”