  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.
