Intermediate quantum maps for quantum computation

Abstract

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production, and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically, and yields pseudorandom operators with original properties, enabling for example to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

4 pages, 4 figures, research done at http://www.quantware.ups-tlse.fr/

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Cited by in corpus (7)

• Distribution of bipartite entanglement for random pure states
• Entanglement in random pure states: Spectral density and average von Neumann entropy
• Multifractal wave functions of simple quantum maps
• Multifractality and intermediate statistics in quantum maps
• Entanglement of localized states
• Quantum computation of multifractal exponents through the quantum wavelet transform
• Quantum computing of semiclassical formulas