A Survey of Quantum Lyapunov Control Methods
The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/967529 |
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| _version_ | 1850216864230146048 |
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| author | Shuang Cong Fangfang Meng |
| author_facet | Shuang Cong Fangfang Meng |
| author_sort | Shuang Cong |
| collection | DOAJ |
| description | The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed. |
| format | Article |
| id | doaj-art-2f34ae18ac6246d99cec2db541a03daf |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-2f34ae18ac6246d99cec2db541a03daf2025-08-20T02:08:12ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/967529967529A Survey of Quantum Lyapunov Control MethodsShuang Cong0Fangfang Meng1Department of Automation, University of Science and Technology of China, Hefei 230027, ChinaDepartment of Automation, University of Science and Technology of China, Hefei 230027, ChinaThe condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed.http://dx.doi.org/10.1155/2013/967529 |
| spellingShingle | Shuang Cong Fangfang Meng A Survey of Quantum Lyapunov Control Methods The Scientific World Journal |
| title | A Survey of Quantum Lyapunov Control Methods |
| title_full | A Survey of Quantum Lyapunov Control Methods |
| title_fullStr | A Survey of Quantum Lyapunov Control Methods |
| title_full_unstemmed | A Survey of Quantum Lyapunov Control Methods |
| title_short | A Survey of Quantum Lyapunov Control Methods |
| title_sort | survey of quantum lyapunov control methods |
| url | http://dx.doi.org/10.1155/2013/967529 |
| work_keys_str_mv | AT shuangcong asurveyofquantumlyapunovcontrolmethods AT fangfangmeng asurveyofquantumlyapunovcontrolmethods AT shuangcong surveyofquantumlyapunovcontrolmethods AT fangfangmeng surveyofquantumlyapunovcontrolmethods |