A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum Factoring, Discrete Logarithms, and the Hidden Subgroup Problem
Computing in Science and Engineering
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Quantum Cryptanalysis of Hash and Claw-Free Functions
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
A lower bound on the quantum query complexity of read-once functions
Journal of Computer and System Sciences
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Coins make quantum walks faster
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-time quantum algorithms for Pell's equation and the principal ideal problem
Journal of the ACM (JACM)
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Complexity of Testing Group Commutativity
Algorithmica
Quantum Algorithms for the Triangle Problem
SIAM Journal on Computing
Any AND-OR Formula of Size N can be Evaluated in time N^{1/2 + o(1)} on a Quantum Computer
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Quantum walks: a comprehensive review
Quantum Information Processing
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Quantum walks are quantum counterparts of random walks. In the last 5 years, they have become one of main methods of designing quantum algorithms. Quantum walk based algorithms include element distinctness, spatial search, quantum speedup of Markov chains, evaluation of Boolean formulas and search on "glued trees" graph. In this talk, I will describe the quantum walk method for designing search algorithms and show several of its applications.