Comment on the paper "Random Quantum Circuits are Approximate 2-designs"

Details Comment on the paper "Random Quantum Circuits are Approximate 2-designs" Comment on the paper "Random Quantum Circuits are Approximate 2-designs"

2010-06-22

arxiv.org/abs/1006.4202v1

Commun. Math. Phys. 304, 281--293 (2011)

Physics

Quantum Physics

Scientific paper

10.1007/s00220-011-1217-x

In [A.W. Harrow and R.A. Low, Commun. Math. Phys. 291, 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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