Pseudorandom generators and the BQP vs. PH problem

@article{Fefferman2010PseudorandomGA,
  title={Pseudorandom generators and the BQP vs. PH problem},
  author={Bill Fefferman and Christopher Umans},
  journal={CoRR},
  year={2010},
  volume={abs/1007.0305}
}
It is a longstanding open problem to devise an oracle relativ to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conje cture about the capacity of the NisanWigderson pseudorandom generator [NW94] to fool AC0, with MAJORITY as its hard function. Our conjecture is essentially that the loss due to the hybrid arg ument (which is a component of the standard proof from [NW94]) can be avoided in this setting. This is a qu estion that has been asked previously in the… CONTINUE READING
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