ONSET OF CHAOS IN A MODEL OF QUANTUM COMPUTATION

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Recently, the question of a relevance of the so-called quantum chaos has been raised in applications to quantum computation [2,3]. Indeed, according to the general approach to closed systems of finite number of interacting Fermi-particles (see, e.g. [4,5]), with an increase of an interaction between qubits a kind of chaos is expected to emerge in the energy spectra and structure of many-body states. Specifically, the fluctuations of energy levels and components of the eigenstates turn out to be very strong and described by the Random Matrix Theory. Clearly, if this happens in a quantum computer, it may lead to a ... continued below

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BERMAN, G. & AL, ET February 1, 2001.

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Recently, the question of a relevance of the so-called quantum chaos has been raised in applications to quantum computation [2,3]. Indeed, according to the general approach to closed systems of finite number of interacting Fermi-particles (see, e.g. [4,5]), with an increase of an interaction between qubits a kind of chaos is expected to emerge in the energy spectra and structure of many-body states. Specifically, the fluctuations of energy levels and components of the eigenstates turn out to be very strong and described by the Random Matrix Theory. Clearly, if this happens in a quantum computer, it may lead to a destruction of the coherence of quantum computations due to internal decoherence inside many-body states. It is important to stress that quantum chaos occurs not only in the systems with random interaction, but also for purely dynamical interaction. In the latter case, the mechanism of chaos is due to a complex (non-linear) form of a two-body interaction represented in the basis of non-interacting particles. Numerical analysis [2] of a simplest model of quantum computer (2D model of 1/2-spins with a random interqubit interaction J) shows that with an increase of the number L of qubits, the chaos threshold J{sub cr} decreases as J{sub cr} {infinity} 1/L. On this ground, it was claimed that the onset of quantum chaos could be dangerous for quantum computers, since their effectiveness requires L >> 1. On the other hand, in [3] it was argued that in order to treat this problem properly, one needs to distinguish between chaotic properties of stationary states, and the dynamical process of quantum computation.

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169 Kilobytes pages

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  • Report No.: LA-UR-01-1157
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 775435
  • Archival Resource Key: ark:/67531/metadc720087

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  • February 1, 2001

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  • Sept. 29, 2015, 5:31 a.m.

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  • March 29, 2016, 8:26 p.m.

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BERMAN, G. & AL, ET. ONSET OF CHAOS IN A MODEL OF QUANTUM COMPUTATION, article, February 1, 2001; New Mexico. (digital.library.unt.edu/ark:/67531/metadc720087/: accessed December 12, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.