Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Quantum Versions of the Yao Principle
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
A lower bound on the quantum query complexity of read-once functions
Journal of Computer and System Sciences
Quantum period reconstruction of approximate sequences
Information Processing Letters
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We consider the problem where P is an unknown permutation on {0, 1...2n-1}, y is in {0, 1...2n-1}, and the goal is to determine the minimum r 0 such that Pr(y) = y. Information about P is available only via queries that yield Px(z) for any x in {0, 1...2m-1} and z in {0, 1...2n-1} (where m is polynomial in n). The main resource under consideration is the number of these queries. We show that the number of queries necessary to solve the problem in the classical probabilistic bounded-error model is exponential in n. This contrasts sharply with the quantum bounded-error model, where a constant number of queries suffice.