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Eigenstates of an operating quantum computer: hypersensitivity to static imperfections |
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| Authors: | G Benenti G Casati S Montangero DL Shepelyansky |
| 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 |
| Abstract: | We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits nq, it is shown that the ideal eigenstates become mixed and strongly modified by static imperfections above a certain threshold which drops exponentially with nq. Above this threshold the quantum eigenstate entropy grows linearly with nq but the computation remains reliable during a time scale which is polynomial in the imperfection strength and in nq. Received 7 March 2002/ Received in final form 3 May 2002 Published online 19 July 2002 |
| Keywords: | PACS 03 67 Lx Quantum computation – 05 45 Mt Semiclassical chaos (“ quantum chaos” ) – 24 10 Cn Many-body theory |
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