Quantum Lower Bounds by Polynomials

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dc.creatorBeals, Robert
dc.creatorBuhrman, Harry
dc.creatorCleve, Richard
dc.creatorMosca, Michele
dc.creatorde Wolf, Ronald
dc.date1998-02-18
dc.date1998-09-30
dc.date.accessioned2026-07-07T06:14:48Z
dc.date.available2026-07-07T06:14:48Z
dc.descriptionWe examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box 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(T^6) 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 so-called 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 and deterministic decision tree complexity.
dc.description10 pages, LaTeX, no figures, final version to appear in FOCS'98
dc.identifierhttps://arxiv.org/abs/quant-ph/9802049
dc.identifierhttp://arxiv.org/abs/quant-ph/9802049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93602
dc.subjectQuantum Physics
dc.subjectComputational Complexity
dc.titleQuantum Lower Bounds by Polynomials
dc.typetext

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