Distribution of interference in random quantum algorithms

Details Distribution of interference in random quantum algorithms Distribution of interference in random quantum algorithms

2006-12-19

arxiv.org/abs/quant-ph/0612168v1

Phys. Rev. A 75, 062314 (2007)

Physics

Quantum Physics

14 pages revtex, 11 eps figures

Scientific paper

10.1103/PhysRevA.75.062314

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 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 efficiently constructing random operators from the Haar measures of CUE or HOE in a high dimensional Hilbert space using universal sets of quantum gates.

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