Statistical properties of eigenvalues for an operating quantum computer with static imperfections |
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Authors: | G Benenti G Casati S Montangero DL Shepelyansky |
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Institution: | (1) International Center for the Study of Dynamical Systems, Università degli Studi dell'Insubria and Istituto Nazionale per la Fisica della Materia, Unità di Como, Via Valleggio 11, 22100 Como, Italy, IT;(2) Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy, IT;(3) Laboratoire de Physique Quantique, Université Paul Sabatier, 31062 Toulouse Cedex 4, France, FR |
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Abstract: | We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates
efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we discuss the quantum
chaos border induced by static imperfections by analyzing the statistical properties of the quantum computer eigenvalues.
For small imperfection strengths the level spacing statistics is close to the case of quasi-integrable systems while above
the border it is described by the random matrix theory. We have found that the border drops exponentially with the number
of qubits, both in the ergodic and quasi-integrable dynamical regimes of the map characterized by a complex phase space structure.
On the contrary, the regime with integrable map dynamics remains more stable against static imperfections since in this case
the border drops only algebraically with the number of qubits.
Received 19 June 2002 / Received in final form 30 September 2002 Published online 17 Decembre 2002
RID="a"
ID="a"e-mail: dima@irsamc.ups-tlse.fr
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ID="b"UMR 5626 du CNRS |
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Keywords: | PACS 03 67 Lx Quantum computation – 05 45 Mt Semiclassical chaos (“ quantum chaos” ) – 24 10 Cn Many-body theory |
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