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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

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.