Quantum
lower bound for recursive Fourier sampling
(pp165-174) S. Aaronson
doi:
https://doi.org/10.26421/QIC3.2-7
Abstracts:
We revisit the oft-neglected `recursive Fourier sampling'
(RFS) problem, introduced by Bernstein and Vazirani to prove an oracle
separation between BPP and BQP. We show that the known quantum algorithm
for RFS is essentially optimal, despite its seemingly wasteful need to
uncompute information. This implies that, to place \mathsf{BQP} outside
of PH[\log] relative to an oracle, one would need to go outside the RFS
framework. Our proof argues that, given any variant of RFS, either the
adversary method of Ambainis yields a good quantum lower bound, or else
there is an efficient classical algorithm. This technique may be of
independent interest.
Key words:
quantum computing, lower bounds, query complexity |