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FOCS

1998

IEEE

1998

IEEE

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...

Related Content

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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