Hamiltonian Identification Through Enhanced Observability Utilizing Quantum Control
This note considers Hamiltonian identification for a controllable quantum system with nondegenerate transitions and a known initial state. We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove tha...
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| Veröffentlicht in: | IEEE transactions on automatic control 2012-10, Vol.57 (10), p.2679-2683 |
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| container_title | IEEE transactions on automatic control |
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| creator | Leghtas, Z. Turinici, G. Rabitz, H. Rouchon, P. |
| description | This note considers Hamiltonian identification for a controllable quantum system with nondegenerate transitions and a known initial state. We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove that the quantum dipole moment matrix is locally observable in the following sense: for any two close but distinct dipole moment matrices, we construct discriminating controls giving two different measurements. This result suggests that what may appear at first to be very restrictive measurements are actually rich for identification, when combined with well designed discriminating controls, to uniquely identify the complete dipole moment of such systems. |
| doi_str_mv | 10.1109/TAC.2012.2190209 |
| format | Article |
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We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove that the quantum dipole moment matrix is locally observable in the following sense: for any two close but distinct dipole moment matrices, we construct discriminating controls giving two different measurements. This result suggests that what may appear at first to be very restrictive measurements are actually rich for identification, when combined with well designed discriminating controls, to uniquely identify the complete dipole moment of such systems.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2012.2190209</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Automatic control ; Classical and quantum physics: mechanics and fields ; Computer science; control theory; systems ; Control equipment ; Control system synthesis ; Control systems ; Control theory. 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We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove that the quantum dipole moment matrix is locally observable in the following sense: for any two close but distinct dipole moment matrices, we construct discriminating controls giving two different measurements. This result suggests that what may appear at first to be very restrictive measurements are actually rich for identification, when combined with well designed discriminating controls, to uniquely identify the complete dipole moment of such systems.</description><subject>Applied sciences</subject><subject>Automatic control</subject><subject>Classical and quantum physics: mechanics and fields</subject><subject>Computer science; control theory; systems</subject><subject>Control equipment</subject><subject>Control system synthesis</subject><subject>Control systems</subject><subject>Control theory. Systems</subject><subject>Dipole moment</subject><subject>Dynamical Systems</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Electric variables measurement</subject><subject>Exact sciences and technology</subject><subject>Hamiltonian identification</subject><subject>Laboratories</subject><subject>Manganese</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Matrices</subject><subject>Modelling and identification</subject><subject>Observability</subject><subject>observability proof</subject><subject>Optimization and Control</subject><subject>Physics</subject><subject>Quantum computation</subject><subject>quantum control</subject><subject>Quantum information</subject><subject>Quantum Physics</subject><subject>Scalars</subject><subject>Stability</subject><subject>Time measurement</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkdFLIzEQxsOhcLXe-8G9LByCPmydZJNs9rEUtUJBDutzyGazNrJNNMkW9K-_lJY--DTMzO8bZuZD6DeGGcbQ3K7nixkBTGYEN0Cg-YEmmDFREkaqMzQBwKJsiOA_0UWMbznllOIJel6qrR2Sd1a54rEzLtneapWsd8V6E_z4uinu3EY5bbriqY0m7FRrB5s-i5eU45d1r8W_Ubk0bouFdyn44RKd92qI5tcxTtHL_d16sSxXTw-Pi_mq1LSCVDJFu66mvaG07wljSrREM1ppRjoMrKbQY8PblrYcOlGzmoMCaLOkFZ0wupqim8PcjRrke7BbFT6lV1Yu5yu5rwHwmvJG7HBmrw_se_Afo4lJbm3UZhiUM36MElec4bwWJRn9-w1982Nw-RKJQQBrBKF1puBA6eBjDKY_bYBB7h2R2RG5d0QeHcmSq-NgFbUa-pC_auNJR7IjFckPmKI_B84aY05tjjnP_eo_Zk6SzA</recordid><startdate>20121001</startdate><enddate>20121001</enddate><creator>Leghtas, Z.</creator><creator>Turinici, G.</creator><creator>Rabitz, H.</creator><creator>Rouchon, P.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Applied sciences Automatic control Classical and quantum physics: mechanics and fields Computer science control theory systems Control equipment Control system synthesis Control systems Control theory. Systems Dipole moment Dynamical Systems Eigenvalues and eigenfunctions Electric variables measurement Exact sciences and technology Hamiltonian identification Laboratories Manganese Mathematical analysis Mathematics Matrices Modelling and identification Observability observability proof Optimization and Control Physics Quantum computation quantum control Quantum information Quantum Physics Scalars Stability Time measurement |
| title | Hamiltonian Identification Through Enhanced Observability Utilizing Quantum Control |
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