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))



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.


Markov Chain Random Permutation Quantum Circuit Versus Distance Reversible Markov Chain 
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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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