English

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

Quantum Physics 2011-05-04 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1006.4202,
  title  = {Comment on the paper "Random Quantum Circuits are Approximate 2-designs"},
  author = {Igor Tuche Diniz and Daniel Jonathan},
  journal= {arXiv preprint arXiv:1006.4202},
  year   = {2011}
}
R2 v1 2026-06-21T15:39:14.613Z