Comment on “Random Quantum Circuits are Approximate 2-designs” by A.W. Harrow and R.A. Low (Commun. Math. Phys. 291, 257–302 (2009))

Springer Science and Business Media LLC - Tập 304 - Trang 281-293 - 2011
Igor Tuche Diniz1,2, Daniel Jonathan1
1Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil
2Institut Néel CNRS, Grenoble, France

Tóm tắt

In [A.W. Harrow and R.A. Low, Commun. Math. Phys. 291(1):257–302 (2009)], it was shown that a quantum circuit composed of random 2-qubit gates converges to an approximate quantum 2-design in polynomial time. We point out and correct a flaw in one of the paper’s main arguments. Our alternative argument highlights the role played by transpositions induced by the random gates in achieving convergence.

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Springer Science and Business Media LLC

Tập 304

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