DocumentCode :
332935
Title :
Quantum lower bounds by polynomials
Author :
Beals, Robert ; Buhrman, Harry ; Cleve, Richard ; Mosca, Michele ; De Wolf, Ronald
Author_Institution :
Dept. of Math., Arizona Univ., Tucson, AZ, USA
fYear :
1998
fDate :
8-11 Nov 1998
Firstpage :
352
Lastpage :
361
Abstract :
We 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(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 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
Keywords :
Boolean functions; computational complexity; quantum computing; Boolean functions; black-box model; characterizations; classical complexity; decision tree complexity; partial functions; polynomial relationship; quantum extension; quantum network; randomized; Computational modeling; Computer science; Hip; Laboratories; Mathematical model; Mathematics; Polynomials; Postal services; Quantum computing; US Department of Transportation;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Foundations of Computer Science, 1998. Proceedings. 39th Annual Symposium on
Conference_Location :
Palo Alto, CA
ISSN :
0272-5428
Print_ISBN :
0-8186-9172-7
Type :
conf
DOI :
10.1109/SFCS.1998.743485
Filename :
743485
Link To Document :
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