A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
Quantum Walk Algorithm for Element Distinctness
SIAM Journal on Computing
Quantum Algorithms for the Triangle Problem
SIAM Journal on Computing
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We study some properties of quantum walks on the plane. First, we discuss the behavior of quantum walks when moving marked locations are introduced. Second, we present an exceptional case, when quantum walk fails to find any of the marked locations.