Algorithmic number theory
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum communication complexity of block-composed functions
Quantum Information & Computation
Property testing for cyclic groups and beyond
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Property testing for cyclic groups and beyond
Journal of Combinatorial Optimization
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We consider the problem where π is an unknown permutation on {0,1,...,2n - 1}, y0 ∈ {0,1,...,2n - 1}, and the goal is to determine the minimum r 0 such that πr(y0)=1. Information about π is available only via queries that yield πx(y) from any x ∈ {0,1,...,2m-1} and y π {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 suffices.