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

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The Original Article was published on 17 July 2009

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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Authors and Affiliations

  1. Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil

    Igor Tuche Diniz & Daniel Jonathan

  2. Institut Néel-CNRS, Grenoble, France

    Igor Tuche Diniz

Authors
  1. Igor Tuche Diniz
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  2. Daniel Jonathan
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Correspondence to Daniel Jonathan.

Additional information

Communicated by M.B. Ruskai

This comment refers to doi:10.1007/s00220-009-0873-6.

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Diniz, I.T., Jonathan, D. Comment on “Random Quantum Circuits are Approximate 2-designs” by A.W. Harrow and R.A. Low (Commun. Math. Phys. 291, 257–302 (2009)). Commun. Math. Phys. 304, 281–293 (2011). https://doi.org/10.1007/s00220-011-1217-x

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