Eur. Phys. J. D 22, 285-293 (2003)
https://doi.org/10.1140/epjd/e2002-00241-9

Statistical properties of eigenvalues for an operating quantum computer with static imperfections

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
² Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
³ Laboratoire de Physique Quantique (UMR 5626 du CNRS) , Université Paul Sabatier, 31062 Toulouse Cedex 4, France

Corresponding author: ^a dima@irsamc.ups-tlse.fr

Received: 19 June 2002
Revised: 30 September 2002
Published online: January 1900

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.