Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Introduction to Recent Quantum Algorithms
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Quantum time-space tradeoffs for sorting
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A new quantum claw-finding algorithm for three functions
New Generation Computing - Quantum computing
ACM SIGACT News
Quantum algorithms a decade after shor
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
On the power of Ambainis lower bounds
Theoretical Computer Science
Improved algorithms for quantum identification of Boolean oracles
Theoretical Computer Science
The quantum query complexity of the determinant
Information Processing Letters
Claw finding algorithms using quantum walk
Theoretical Computer Science
Quantum sampling for balanced allocations
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
The quantum complexity of group testing
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Quantum algorithms for subset finding
Quantum Information & Computation
Promised and distributed quantum search
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
The quantum query complexity of AC0
Quantum Information & Computation
The quantum query complexity of algebraic properties
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
An improved claw finding algorithm using quantum walk
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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Abstract: We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Hyer, and Tapp, and imply an O(N^{3/4} log N) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with \Theta(N log N) classical complexity. We also prove a lower bound of \Omega(\sqrt N) comparisons for this problem and derive bounds for a number of related problems.