A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous. One-dimensional quantum walks. In Proc. 37--49, 2001. Home/Search Document Details and Download
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Quantum Walks on the Hypercube - Moore, Russell (2002) (1 citation) (Correct)
....then, it is natural to ask if a quantum walk can mix more quickly than its classical counterpart. Since a unitary process cannot be mixing, we define a stochastic process from a quantum one by performing a measurement at a given time or a distribution of times. Several recent articles [AAKV01, ABN 01, NV00] have answered this question in the affirmative, showing, for example, that a quantum walk on the n cycle mixes in time O(nlogn) a substantial improvement over the classical random walk which requires Q(n 2 ) steps to mix. Quantum walks were also defined in [Wat01] and used to show ....
....of quantum LOGSPACE. These articles raise the exciting possibility that quantum Monte Carlo algorithms could form a new family of quantum algorithms that work more quickly than their classical counterparts. Two types of quantum walks exist in the literature. The first, introduced by [AAKV01, ABN 01, NV00] studies the behavior of a directed particle on the graph; we refer to these as discrete time quantum walks. The second, introduced in [FG98, CFG01] defines the dynamics by treating the adjacency matrix of the graph as a Hamiltonian; we refer to these as continuous time quantum walks. ....
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Andris Ambainis, Eric Bach, Ashwin Nayak, Ashvin Vishwanath, and John Watrous. Onedimensional quantum walks. In ACM [ACM01].
Exponential Algorithmic Speedup by a Quantum Walk - Andrew Childs Richard (Correct)
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A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous. One-dimensional quantum walks. In Proc. 37--49, 2001.
Exponential Algorithmic Speedup by a Quantum Walk - Childs, Cleve, Deotto.. (2 citations) (Correct)
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A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous. One-dimensional quantum walks. In Proc. 37--49, 2001.
Quantum Computing Classical Physics - Meyer (2001) (Correct)
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A. Ambainis, E. Bach, A. Nayak, A. Vishwanath and J. Watrous, "One dimensional quantum walks", in Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, Hersonissos, Crete, Greece, 6--8 July 2001.
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