Delocalization border and onset of chaos in a model of quantum computation

G. P. Berman, F. Borgonovi, F. M. Izrailev, and V. I. Tsifrinovich
Phys. Rev. E 64, 056226 – Published 25 October 2001
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Abstract

We study the properties of spectra and eigenfunctions for a chain of 1/2 spins (qubits) in an external time-dependent magnetic field and under the conditions of nonselective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transitions and show that for the interaction between nearest qubits, the transition is very different from that in quantum chaos. We explain this phenomena by showing that in the considered region of parameters our model is close to an integrable one. According to a general opinion, the threshold for the onset of quantum chaos due to the interqubit interaction decreases with an increase of the number of qubits. Contrary to this expectation, for a magnetic field with constant gradient we have found that chaos border does not depend on the number of qubits. We give analytical estimates that explain this effect, together with numerical data supporting our analysis. Random models with long-range interactions have been studied as well. In particular, we show that in this case the delocalization and quantum chaos borders coincide.

  • Received 29 March 2001

DOI:https://doi.org/10.1103/PhysRevE.64.056226

©2001 American Physical Society

Authors & Affiliations

G. P. Berman1, F. Borgonovi2,3, F. M. Izrailev4, and V. I. Tsifrinovich5

  • 1Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
  • 2Dipartimento di Matematica e Fisica, Università Cattolica, via Musei 41, 25121 Brescia, Italy
  • 3INFM, Gruppo Collegato di Brescia and INFN, Sezione di Pavia Italy
  • 4Instituto de Fisica, Universidad Autonoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
  • 5IDS Department, Polytechnic University, Six Metrotech Center, Brooklyn, New York 11201

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Vol. 64, Iss. 5 — November 2001

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