Communications in Mathematical Physics

, Volume 304, Issue 1, pp 281–293 | Cite as

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

Article

Abstract

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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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal FluminenseNiteróiBrazil
  2. 2.Institut Néel-CNRSGrenobleFrance

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