Efficiency of producing random unitary matrices with quantum circuits

Ludovic Arnaud and Daniel Braun
Phys. Rev. A 78, 062329 – Published 17 December 2008

Abstract

We study the scaling of the convergence of several statistical properties of a recently introduced random unitary circuit ensemble towards their limits given by the circular unitary ensemble. Our study includes the full distribution of the absolute square of a matrix element, moments of that distribution up to order eight, as well as correlators containing up to 16 matrix elements in a given column of the unitary matrices. Our numerical scaling analysis shows that all of these quantities can be reproduced efficiently, with a number of random gates which scales at most as nq[ln(nqϵ)]ν with the number of qubits nq for a given fixed precision ϵ and ν>0.

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  • Received 4 July 2008

DOI:https://doi.org/10.1103/PhysRevA.78.062329

©2008 American Physical Society

Authors & Affiliations

Ludovic Arnaud and Daniel Braun

  • Laboratoire de Physique Théorique, IRSAMC, UPS, CNRS, Université de Toulouse, F-31062 Toulouse, France

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Issue

Vol. 78, Iss. 6 — December 2008

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