Oracle Separation of BQP and PH

Electronic Colloquium on Computational Complexity (ECCC), Volume 25, 2018, Pages 13-23.

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Keywords:
BQP bounded depth circuits oracle separation polynomial hierarchy

Abstract:

We present a distribution D over inputs in {−1,1}2N, such that: (1) There exists a quantum algorithm that makes one (quantum) query to the input, and runs in time O(logN), that distinguishes between D and the uniform distribution with advantage Ω(1/logN). (2) No Boolean circuit of quasi-polynomial size and constant depth distinguishes bet...More

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