Convergence Conditions for Random Quantum Circuits

Details Convergence Conditions for Random Quantum Circuits Convergence Conditions for Random Quantum Circuits

2005-03-28

arxiv.org/abs/quant-ph/0503210v3

Phys. Rev. A 72, 060302 (2005)

Physics

Quantum Physics

4 pages (revtex), comments welcome. v2: reference added, title changed; v3: published version, minor changes, references updat

Scientific paper

10.1103/PhysRevA.72.060302

Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical framework for analyzing pseudo-random ensembles generated through a random circuit composition. We prove that the measure over random circuits converges exponentially (with increasing circuit length) to the uniform (Haar) measure on the unitary group and describe how the rate of convergence may be calculated for specific applications.

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