Distribution of interference in random quantum algorithms

Journal Article · Fri Jun 15 04:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.75.062314· OSTI ID:20991099

Arnaud, Ludovic; Braun, Daniel ^[1]

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1. Laboratoire de Physique Theorique, IRSAMC, UMR 5152 du CNRS, Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse (France)

We study the amount of interference in random quantum algorithms using a recently derived quantitative measure of interference. To this end we introduce two random circuit ensembles composed of random sequences of quantum gates from a universal set, mimicking quantum algorithms in the quantum circuit representation. We show numerically that, concerning the interference distribution and the level spacing distribution, these ensembles converge to the well-known circular unitary ensemble (CUE) for general complex quantum algorithms, and to the Haar orthogonal ensemble (HOE) for real quantum algorithms. We provide exact analytical formulas for the average and typical interference in the circular ensembles, and show that for sufficiently large numbers of qubits a random quantum algorithm uses with probability close to one an amount of interference approximately equal to the dimension of the Hilbert space. As a by-product, we offer a new way of constructing approximate random unitary operators from the Haar measures of CUE or HOE in a high dimensional Hilbert space using universal sets of quantum gates.

• OSTI ID: 20991099
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 75; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
DISTRIBUTION
HILBERT SPACE
INTERFERENCE
PROBABILITY
QUBITS
RANDOMNESS