Novotny, Jaroslav ; Alber, Gernot ; Jex, Igor (2010)
Asymptotic Evolution of Random Unitary Operations.
In: Central European Journal of Physics, 8 (6)
doi: 10.2478/s11534-010-0018-8
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2010 |
| Autor(en): | Novotny, Jaroslav ; Alber, Gernot ; Jex, Igor |
| Art des Eintrags: | Bibliographie |
| Titel: | Asymptotic Evolution of Random Unitary Operations |
| Sprache: | Deutsch |
| Publikationsjahr: | Februar 2010 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Central European Journal of Physics |
| Jahrgang/Volume einer Zeitschrift: | 8 |
| (Heft-)Nummer: | 6 |
| DOI: | 10.2478/s11534-010-0018-8 |
| Kurzbeschreibung (Abstract): | We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits. |
| ID-Nummer: | TUD-CS-2010-2450 |
| Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik |
| Hinterlegungsdatum: | 30 Dez 2016 20:23 |
| Letzte Änderung: | 10 Mai 2022 07:31 |
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