Pseudorandom generators and the BQP vs. PH problem

It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture 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 argument (which is a component of the standard proof from [NW94]) can be avoided in this setting. This is a question that has been asked previously in the pseudorandomness literature [BSW03]. We then make three main contributions:

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Bill Fefferman, Christopher Umans
• Keywords: CORR 2010, Education, Longstanding Open Problem, NisanWigderson Pseudorandom Generator, Polynomial-time Hierarchy