Subspace Stabilization Analysis for Non-Markovian Open Quantum Systems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866916533628829696 |
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| author | Zhang, Shikun Liu, Kun Dong, Daoyi Feng, Xiaoxue Pan, Feng |
| author_facet | Zhang, Shikun Liu, Kun Dong, Daoyi Feng, Xiaoxue Pan, Feng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_10088 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Subspace Stabilization Analysis for Non-Markovian Open Quantum Systems Zhang, Shikun Liu, Kun Dong, Daoyi Feng, Xiaoxue Pan, Feng Quantum Physics Systems and Control 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. |
| title | Subspace Stabilization Analysis for Non-Markovian Open Quantum Systems |
| topic | Quantum Physics Systems and Control |
| url | https://arxiv.org/abs/1901.10088 |