Scott Aaronson  Home/Search
Context Related
Links: ACM DBLP | berkeley.edu/~aaron...aaronson47057.ps Cached: PS.gz PS PDF This document uses CoBlitz to cache paper downloads. If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
Image Update HelpPS.gz PS PDF From: berkeley.edu/~aaronson...research (more) (Enter author homepages) |
Rate this article:      (best)Comment on this article |
Abstract: The collision problem is to decide whether a function X : . . . , n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of on the number of queries needed by a quantum computer to solve this problem with bounded error probability. The best known upper bound is O , but obtaining any lower bound better than# (1) was an open problem since 1997. Our proof uses the polynomial method augmented by some new ideas. We also give a lower bound for... (Update)
Cited by: More
Adiabatic Quantum State Generation and Statistical Zero.. - Aharonov, Ta-Shma (2003) (Correct)
Lower Bounds for Local Search by Quantum Arguments - Aaronson (2004) (Correct)
Limitations of Quantum Advice and One-Way Communication - Aaronson (2004) (Correct)
Active bibliography (related documents): More All
0.6: Quantum Certificate Complexity - Aaronson (Correct)
0.5: Finding Solutions to NP Problems: Philosophical Differences.. - Greenwood (2001) (Correct)
0.3: Average-Case Quantum Query Complexity - Ambainis, de Wolf (2000) (Correct)
Similar documents based on text: More All
0.2: Almost-Everywhere Superiority for Quantum Computing - Hemaspaandra, Hemaspaandra.. (1999) (Correct)
0.2: Quantum Algorithms for Element Distinctness - Buhrman, Dürr, Heiligman.. (2000) (Correct)
0.2: Multilinear Formulas and Skepticism of Quantum Computing - Aaronson (2004) (Correct)
Related documents from co-citation: More All
5: Quantum Lower Bounds by Polynomials - Beals, Buhrman et al.
5: Strengths and weaknesses of quantum computing - Charles, Ethan et al.
4: Quantum lower bounds by quantum arguments - Ambainis
BibTeX entry: (Update)
S. Aaronson. Quantum lower bound for the col- lision problem, in Proc. ACM $TOC'2002. http://citeseer.ist.psu.edu/aaronson02quantum.html More
@misc{ aaronson02quantum,
author = "S. Aaronson",
title = "Quantum lower bound for the col- lision problem",
text = "S. Aaronson. Quantum lower bound for the col- lision problem, in Proc.
ACM $TOC'2002.",
year = "2002",
url = "citeseer.ist.psu.edu/aaronson02quantum.html" }
Citations (may not include all citations):210 A fast quantum mechanical algorithm for database search - Grover - 1996 ACM DBLP
173 Quantum complexity theory - Bernstein, Vazirani - 1997 ACM DBLP
164 Polynomial-time algorithms for prime factorization and discr.. - Shor - 1997 ACM DBLP
144 the power of quantum computation - Simon - 1994
103 Introduction to approximation theory (context) - Cheney - 1966
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
56 Collision free hash functions and public key signature schem.. (context) - Damgard - 1988 DBLP
49 Quantum lower bounds by polynomials - Beals, Buhrman et al. - 1998 ACM DBLP
44 CREW PRAMs and decision trees (context) - Nisan - 1991 ACM DBLP
40 Quantum measurements and the abelian stabilizer problem (context) - Kitaev - 1996 DBLP
27 A complete promise problem for statistical zero-knowledge - Sahai, Vadhan - 1997 ACM DBLP
23 On quantum algorithms for noncommutative hidden subgroups - Ettinger, Hyer - 2000 ACM DBLP
21 Cryptographic hash functions: a survey - Bakhtiari, Safavi-Naini et al. - 1995
17 Complexity measures and decision tree complexity: a survey - Buhrman, de Wolf - 2002 DBLP
16 Quantum mechanical algorithms for the nonabelian hidden subg.. - Grigni, Schulman et al. - 2001 ACM DBLP
16 Quantum lower bounds by quantum arguments - Ambainis - 2000 ACM DBLP
16 Schwankung von Polynomen zwischen Gitterpunkten (context) - Ehlich, Zeller - 1964
15 Quantum algorithm for the collision problem - Brassard, Hyer et al. - 1997
11 A comparison of Uniform Approximations on an interval and a .. (context) - Rivlin, Cheney - 1966
7 Succinct quantum proofs for properties of finite groups - Watrous - 2000 ACM DBLP
5 Quantum algorithms for element distinctness - Buhrman, Durr et al. - 2001 ACM DBLP
4 Quantum lower bounds for the collision and the element disti.. (context) - Shi - 2001 ACM DBLP
3 Talk given at (context) - Rains - 1997
2 Quantum Information Science (context) - Foundation - 1999
1 the power of quantum oracles (context) - Kashefi, Kent et al. - 2001
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.cs.berkeley.edu/~aaronson/research.html): More
Algorithms for Boolean Function Query Properties - Aaronson (Correct)
Quantum Computing and Dynamical Quantum Models - Aaronson (Correct)
BOOK REVIEW on A New Kind of Science by Stephen Wolfram Wolfram - Aaronson (2001) (Correct)
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC