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Abstract: We examine the number T of queries that a quantum network requires to compute several Boolean functions on f0; 1g N 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... (Update)
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BibTeX entry: (Update)
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, Ronald de Wolf "Quantum Lower Bounds by Polynomials", quantph /9802049. http://citeseer.ist.psu.edu/article/beals98quantum.html More
@inproceedings{ beals98quantum,
author = "Robert Beals and Harry Buhrman and Richard Cleve and Michele Mosca and Ronald de Wolf",
title = "Quantum Lower Bounds by Polynomials",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "352-361",
year = "1998",
url = "citeseer.ist.psu.edu/article/beals98quantum.html" }
Citations (may not include all citations):210 A fast quantum mechanical algorithm for database search - Grover - 1996
164 Polynomial-time algorithms for prime factorization and discr.. - Shor - 1997 ACM DBLP
144 the power of quantum computation - Simon - 1997
126 Rapid solution of problems by quantum computation (context) - Deutsch, Jozsa - 1992 ACM
102 Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997 ACM DBLP
57 the degree of Boolean functions as real polynomials - Nisan, Szegedy - 1994
50 Quantum algorithms revisited - Cleve, Ekert et al. - 1998
46 An exact quantum polynomialtime algorithm for Simon's proble.. - Brassard, Hoyer - 1997
40 Quantum measurements and the Abelian stabilizer problem (context) - Kitaev - 1995 DBLP
36 Complexity limitations on quantum computation - Fortnow, Rogers - 1998 ACM DBLP
35 Quantum cryptanalysis of hidden linear functions (context) - Boneh, Lipton - 1995
32 An oracle builder's toolkit - Fenner, Fortnow et al. - 1993 ACM DBLP
31 The polynomial method in circuit complexity - Beigel - 1993 DBLP
31 Personal communication (context) - van Melkebeek - 1998
30 Quantum counting - Brassard, Hoyer et al. - 1998
29 Probabilistic Boolean decision trees and the complexity of e.. (context) - Saks, Wigderson - 1986 DBLP
23 The hidden subgroup problem and eigenvalue estimation on a q.. - Mosca, Ekert - 1998
21 Grover's quantum searching algorithm is optimal (context) - Zalka - 1997
18 the degree of polynomials that approximate symmetric Boolean.. (context) - Paturi - 1992
16 Schwankung von Polynomen zwischen Gitterpunkten (context) - Ehlich, Zeller - 1964
11 Earlier version in STOC (context) - Nisan, decision et al. - 1991
11 A comparison of uniform approximations on an interval and a .. (context) - Rivlin, Cheney - 1966
11 the Monte Carlo decision tree complexity of read-once formul.. (context) - Santha - 1991
10 counting and amplitude amplification by eigenvector analysis (context) - Mosca - 1998
8 Personal communication (context) - Nisan - 1998
7 Personal communication (context) - Hayes, Kutin - 1998
4 Personal communication (context) - Ambainis - 1998
3 Personal communication (context) - Terhal - 1997
3 Polynomials with two values (context) - Gathen, Roche - 1997
2 Earlier version in Physcomp'96; also quant-ph (context) - Boyer, Brassard et al. - 1998
2 Conjugated operators in quantum algorithms - Hoyer - 1997 ACM
2 Quantum oracle interrogation: Getting all information for al.. (context) - van Dam - 1998
1 Personal communication (context) - Hoyer - 1998
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