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Accueil du site > Publications > Publications 2008 > Efficiency of Producing Random Unitary Matrices with Quantum Circuits

Efficiency of Producing Random Unitary Matrices with Quantum Circuits

Ludovic Arnaud and Daniel Braun

par Daniel Braun - 17 mars 2009

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 n_q(\ln n_q /\epsilon)^\nu with the number of qubits n_q for a given fixed precision \epsilon and \nu>0.