Scalable ROM-PRUs imply a positive resolution to the Aaronson-Kuperberg unitary synthesis problem, with any such algorithm requiring a classical oracle of input length (2-o(1))log d that rules out existing candidates.
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On Scalable Pseudorandom Unitaries and the Unitary Synthesis Problem
Scalable ROM-PRUs imply a positive resolution to the Aaronson-Kuperberg unitary synthesis problem, with any such algorithm requiring a classical oracle of input length (2-o(1))log d that rules out existing candidates.