Subspace stabilization analysis for a class of non-Markovian open quantum systems

Shikun Zhang, Kun Liu*, Daoyi Dong, Xiaoxue Feng, Feng Pan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Studied in this article is non-Markovian open quantum systems parametrized by Hamiltonian H, coupling operator L, and memory kernel function γ, which is a proper candidate for describing the dynamics of various solid-state quantum information processing devices. We look into the subspace stabilization problem of the system from the perspective of dynamical systems and control. The problem translates itself into finding analytic conditions that characterize invariant and attractive subspaces. Necessary and sufficient conditions are found for subspace invariance based on algebraic computations, and sufficient conditions are derived for subspace attractivity by applying a double integral Lyapunov functional. Mathematical proof is given for those conditions and a numerical example is provided to illustrate the theoretical result.

Original languageEnglish
Article number042327
JournalPhysical Review A
Volume101
Issue number4
DOIs
Publication statusPublished - Apr 2020

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