Quantum Lower Bounds by Polynomials

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Quantum Lower Bounds by Polynomials
We examine the number T of queries that a quantum network requires to compute several Boolean functions on f0;1gN in the black-box model. We show that, in the blackbox model, the exponential quantum speed-up obtained for partial functions (i.e. problems involving a promise on the input) by Deutsch and Jozsa and by Simon cannot be obtained for any total function: if a quantum algorithm computes some total Boolean function f with bounded-error using T black-box queries then there is a classical deterministic algorithm that computes f exactly with O(T6) queries. We also give asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings. Finally, we give new precise bounds for AND, OR, and PARITY. Our results are a quantum extension of the socalled polynomial method, which has been successfully applied in classical complexity theory, and also a quantum extension of results by Nisan about a polynomial relationship between randomized an...
Robert Beals, Harry Buhrman, Richard Cleve, Michel
Added 04 Aug 2010
Updated 04 Aug 2010
Type Conference
Year 1998
Where FOCS
Authors Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, Ronald de Wolf
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