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Abstract: this paper, we have in looked into some theoritical problems and tried to see how quantum algorithms performs in those cases. We have shown that collision-finding as well as element-distinctness problem cannot be done better than N). Our algorithm for collision detection takes O(N log n) queries, and so there remains the gap between the upper and lower bound which needs to be closed. The maximum finding problem uses N) steps - which may be used to find some kth largest (or smallest... (Update)
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0.4: Average-Case Quantum Query Complexity - Ambainis, de Wolf (2000) (Correct)
0.3: Quantum Lower Bound for the Collision Problem - Aaronson (2002) (Correct)
0.2: Quantum Lower Bounds by Quantum Arguments - Ambainis (Correct)
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BibTeX entry: (Update)
@misc{ chakraborty-quantum,
author = "Arindam Chakraborty and Debajyoti Bera",
title = "Quantum Algorithms",
url = "citeseer.ist.psu.edu/chakraborty02quantum.html" }
Citations (may not include all citations):210 A fast quantum mechanical algorithm for database search - Grover - 1996
167 Quantum Computation and Quantum Information (context) - Michael, Nielsen - 2000
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
30 Quantum counting - Brassard, Tapp - 1998 ACM DBLP
16 Quantum lower bounds by quantum arguments - Ambainis - 2000
15 Quantum algorithm for the collision problem - Brassard, Hyer et al. - 1997
11 Quantum amplitude amplification and estimation - Brassard, Hyer et al.
5 Quantum algorithms for element distinctness - Buhrman, Durr et al. - 2001 ACM DBLP
1 A quantum algorithm for finding the minimum (context) - Drr, Hyer
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