We report an error found in this Letter: In Sec. V, there is both a typographic error in Theorem 3 as well as a false statement concerning the speed of convergence of the expander graph construction that we present in the section. The relevant scaling is exponential with the system size (i.e., the logarithm of the Hilbert-space dimension) rather than with the Hilbert-space dimension of the source of randomness R, as originally claimed. There are corresponding typographic errors in the statement of Theorem 3, in which every occurrence of the term 8k should be corrected to 8k. Furthermore, in the statement of the theorem, it should read U ∈ Ued8kT instead of U ∈ ed8kT, UenT denoting the group of n × n unitary matrices. Given these corrections to the statement of the theorem, the theorem is correct and so is the proof.
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