E. Farhi and S. Gutmann. Quantum computation and decision trees. Phys. Rev. A, 58:915--928, 1998.  Home/Search   Document Not in Database   Summary   APS   Related Articles   Check

....[4, 5] This gives another asymptotic form for the probability distribution. The SchrSdinger approach is also quite general and could be potentially applied to quantum walks on any Cayley graph. Related work Various quantum variants of random walks have previously been studied by a few authors [6, 12, 24, 32], but their results are, for the most part, unrelated to ours. The first study of quantum walks is apparently due to Meyer [24] Meyer s model (quantum lattice gas automata or QLGA) is equivalent to our two way infinite Hadamard walk, but he addresses different questions than the ones we ....

....we state as Lemma 4) Meyer proceeds to analyzing the continuoustime limit of QLGA and shows that this limit is given by the Dirac equation [13] The results about the continuous time limit apparently do not imply anything for the discrete case that we study in this paper. Farhi and Gutmann [12] and Childs, Farhi and Gutmann [6] analyze quantum walks on trees and exhibit collections of graphs on which the quantum process hits one particular node exponentially faster than the corresponding classical process. The definition for quantum walks considered in these papers is completely ....

E. Faxhi and S. Gutmann. Quantum computation and decision trees. Physical Review A, 58:915-928, 1998.

....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. The landscape is further complicated by the existence of two distinct notions of mixing time. The instantaneous notion [ABN 01, NV00] focuses on ....

.... can be applied [Dia88] Below we will use some aspects of this approach, especially the Diaconis Shahshahani bound on the total variation distance [DS81] For simplicity, we restrict our discussion to quantum walks on Cayley graphs; more general treatments of quantum walks appear in [AAKV01, FG98] Before describing the quantum walk models we set down some notation. For a group G and a set of generators G such that G = G 1 , let X(G;G) denote the undirected Cayley graph of G with respect to G. For a finite set S, we let L(S) f f : S C g denote the collection of C valued functions ....

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Edward Farhi and Sam Gutmann. Quantum computation and decision trees. Phys. Rev. A, 58:915--, 1998.

....[4, 5] This gives another asymptotic form for the probability distribution. The Schr odinger approach is also quite general and could be potentially applied to quantum walks on any Cayley graph. Related work Various quantum variants of random walks have previously been studied by a few authors [6, 12, 24, 32], but their results are, for the most part, unrelated to ours. The rst study of quantum walks is apparently due to Meyer [24] Meyer s model (quantum lattice gas automata or QLGA) is equivalent to our two way in nite Hadamard walk, but he addresses di erent questions than the ones we consider. ....

....we state as Lemma 4) Meyer proceeds to analyzing the continuoustime limit of QLGA and shows that this limit is given by the Dirac equation [13] The results about the continuous time limit apparently do not imply anything for the discrete case that we study in this paper. Farhi and Gutmann [12] and Childs, Farhi and Gutmann [6] analyze quantum walks on trees and exhibit collections of graphs on which the quantum process hits one particular node exponentially faster than the corresponding classical process. The de nition for quantum walks considered in these papers is completely di erent ....

E. Farhi and S. Gutmann. Quantum computation and decision trees. Physical Review A, 58:915-928, 1998.

.... paper we are only considering one way to de ne quantum random walks, and it should be noted that we are not suggesting that this is the only de nition there are several ways one can de ne quantum variations on random walks (see, for instance, the quantum processes considered by Farhi and Gutmann [4]) 1.1 Related work Quantum random walks have been studied by Meyer [11] and Farhi and Gutmann [4] but their results are mostly unrelated to ours. Meyer s model (quantum lattice gas automata or QLGA) is the same as our two way in nite quantum random walk but the questions that he asks are quite ....

....we are not suggesting that this is the only de nition there are several ways one can de ne quantum variations on random walks (see, for instance, the quantum processes considered by Farhi and Gutmann [4] 1. 1 Related work Quantum random walks have been studied by Meyer [11] and Farhi and Gutmann [4] but their results are mostly unrelated to ours. Meyer s model (quantum lattice gas automata or QLGA) is the same as our two way in nite quantum random walk but the questions that he asks are quite di erent from ours. The only overlapping result is the formula for the amplitudes as the sum of ....

[Article contains additional citation context not shown here]

E. Farhi and S. Gutmann. Quantum computation and decision trees. Physical Review A, 58:915{ 928, 1998.

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E. Farhi and S. Gutmann. Quantum computation and decision trees. Phys. Rev. A, 58:915--928, 1998.

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E. Farhi and S. Gutmann. Quantum computation and decision trees. Phys. Rev. A, 58:915--928, 1998.

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E. Farhi and S. Gutmann, "Quantum computation and decision trees", Phys. Rev. A 58 (1998) 915--928.

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