Title

Irreversibility And Entanglement Spectrum Statistics In Quantum Circuits

Keywords

entanglement in extended quantum systems (theory); quantum chaos

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 non-universal 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.

Publication Date

12-1-2014

Publication Title

Journal of Statistical Mechanics: Theory and Experiment

Volume

2014

Issue

12

Number of Pages

-

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/1742-5468/2014/12/P12007

Socpus ID

84916622930 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84916622930

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