Eur. Phys. J. D 17, 265-272 (2001)
https://doi.org/10.1007/s100530170031

Emergence of Fermi-Dirac thermalization in the quantum computer core

¹ Laboratoire de Physique Quantique (UMR 5626 du CNRS) , Université Paul Sabatier, 31062 Toulouse Cedex 4, France
² International Center for the Study of Dynamical Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
³ Istituto Nazionale di Fisica della Materia, Unità di Como, via Valleggio 11, 22100 Como, Italy
⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy

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

Received: 3 July 2001
Revised: 9 September 2001
Published online: 15 November 2001

Abstract

We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. In the limit when fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure and we study the quantum computer core (central band) with the highest density of states. Above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of eigenstates in an isolated quantum computer. The onset of chaos results in the interaction induced dynamical thermalization and the occupation numbers well described by the Fermi-Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability.