Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Bounded round interactive proofs in finite groups
SIAM Journal on Discrete Mathematics
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Relativized separation of EQP from PNP
Information Processing Letters
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract)
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Succinct quantum proofs for properties of finite groups
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Parity, circuits, and the polynomial-time hierarchy
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
On the power of quantum computation
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Quantum and classical tradeoffs
Theoretical Computer Science
Quantum algorithms for highly non-linear Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The polynomial degree of recursive Fourier sampling
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Quantum lower bound for recursive fourier sampling
Quantum Information & Computation
Super-polynomial quantum speed-ups for boolean evaluation trees with hidden structure
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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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 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.