Irreversibility and entanglement spectrum statistics in quantum circuits

    Authors

    D. Shaffer; C. Chamon; A. Hamma;E. R. Mucciolo

    Comments

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    Abbreviated Journal Title

    J. Stat. Mech.-Theory Exp.

    Keywords

    quantum chaos; entanglement in extended quantum systems (theory); Mechanics; Physics, Mathematical

    Abstract

    We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a nonuniversal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.

    Journal Title

    Journal of Statistical Mechanics-Theory and Experiment

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    15

    WOS Identifier

    WOS:000348709800007

    ISSN

    1742-5468

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