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ALGORITHMICA
2002

Sharp Quantum versus Classical Query Complexity Separations

8 years 6 months ago
Sharp Quantum versus Classical Query Complexity Separations
We obtain the strongest separation between quantum and classical query complexity known to date--specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved exactly in the quantum case with a single query (and a polynomial number of auxiliary operations). The problem is simple to define and the quantum algorithm solving it is also simple when described in terms of certain quantum Fourier transforms (QFTs) that have natural properties with respect to the algebraic structures of finite fields. These QFTs may be of independent interest, and we also investigate generalizations of them to noncommutative finite rings. Key Words. Quantum algorithms, Quantum Fourier transform.
J. Niel de Beaudrap, Richard Cleve, John Watrous
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2002
Where ALGORITHMICA
Authors J. Niel de Beaudrap, Richard Cleve, John Watrous
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