dorsal/arxiv
View SchemaFeedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds
| Authors | Claudio Altafini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506268 |
| URL | https://arxiv.org/abs/quant-ph/0506268 |
| DOI | 10.1109/TAC.2007.908306 |
| Journal | IEEE Transactions on Automatic Control, 52(11):2019-2028, 2007 |
Abstract
In an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a ``root-space''-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability.
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"abstract": "In an N-level quantum mechanical system, the problem of unitary feedback\nstabilization of mixed density operators to periodic orbits admits a natural\nLyapunov-based time-varying feedback design. A global description of the domain\nof attraction of the closed-loop system can be provided based on a\n``root-space\u0027\u0027-like structure of the space of density operators. This convex\nset foliates as a complex flag manifold where each leaf is identified with the\ncoadjoint orbit of the eigenvalues of the density operator. The converging\nconditions are time-independent but depend from the topology of the flag\nmanifold: it is shown that the closed loop must have a number of equilibria at\nleast equal to the Euler characteristic of the manifold, thus imposing\nobstructions of topological nature to global stabilizability.",
"arxiv_id": "quant-ph/0506268",
"authors": [
"Claudio Altafini"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TAC.2007.908306",
"journal_ref": "IEEE Transactions on Automatic Control, 52(11):2019-2028, 2007",
"title": "Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds",
"url": "https://arxiv.org/abs/quant-ph/0506268"
},
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