Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed
We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed. For a generic Lindblad master equation, we introduce a diss...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2014
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| Online Access: | http://hdl.handle.net/1721.1/83937 https://orcid.org/0000-0003-3207-594X |
| _version_ | 1826216632582668288 |
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| author | Cappellaro, Paola Ticozzi, Francesco Lucchese, Riccardo Viola, Lorenza |
| author2 | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Cappellaro, Paola Ticozzi, Francesco Lucchese, Riccardo Viola, Lorenza |
| author_sort | Cappellaro, Paola |
| collection | MIT |
| description | We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed. For a generic Lindblad master equation, we introduce a dissipation-induced decomposition of the associated Hilbert space, and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence. The resulting design principles are illustrated in realistic Markovian control settings motivated by quantum information processing, including quantum-optical systems and nitrogen-vacancy centers in diamond. |
| first_indexed | 2024-09-23T16:50:15Z |
| format | Article |
| id | mit-1721.1/83937 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:50:15Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/839372022-09-29T21:52:12Z Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed Cappellaro, Paola Ticozzi, Francesco Lucchese, Riccardo Viola, Lorenza Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Capellaro Paola Cappellaro, Paola We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed. For a generic Lindblad master equation, we introduce a dissipation-induced decomposition of the associated Hilbert space, and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence. The resulting design principles are illustrated in realistic Markovian control settings motivated by quantum information processing, including quantum-optical systems and nitrogen-vacancy centers in diamond. 2014-01-13T20:54:47Z 2014-01-13T20:54:47Z 2012-08 2011-01 Article http://purl.org/eprint/type/JournalArticle 0018-9286 1558-2523 http://hdl.handle.net/1721.1/83937 Ticozzi, F., R. Lucchese, P. Cappellaro, and L. Viola. “Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed.” IEEE Transactions on Automatic Control 57, no. 8 (August 2012): 1931-1944. https://orcid.org/0000-0003-3207-594X en_US http://dx.doi.org/10.1109/TAC.2012.2195858 IEEE Transactions on Automatic Control Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) Prof. Cappellaro via Chris Sherratt |
| spellingShingle | Cappellaro, Paola Ticozzi, Francesco Lucchese, Riccardo Viola, Lorenza Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed |
| title | Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed |
| title_full | Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed |
| title_fullStr | Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed |
| title_full_unstemmed | Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed |
| title_short | Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed |
| title_sort | hamiltonian control of quantum dynamical semigroups stabilization and convergence speed |
| url | http://hdl.handle.net/1721.1/83937 https://orcid.org/0000-0003-3207-594X |
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