A. Childs, E. Faxhi, S. Gutmann. An example of the difference between quantum and classical random walks. LANL preprint axchive, quant-ph/0103020. Home/Search Document Not in Database Summary Related Articles Check |
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One-Dimensional Quantum Walks - Ambainis, Bach, Nayak, Vishwanath.. (3 citations) (Correct)
....[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 ....
....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 different from ours. One of us [32] has ....
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A. Childs, E. Faxhi, S. Gutmann. An example of the difference between quantum and classical random walks. LANL preprint axchive, quant-ph/0103020.
Quantum Walks on the Hypercube - Moore, Russell (2002) (1 citation) (Correct)
....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 ....
....since U t = e iHt = 1 In fact, this limit exists under more general circumstances; see e.g. MR95] 2 1 iHt (iHt) 2 =2 , the amplitude of making s steps is the coefficient (it) s =s of H s , which up to normalization is Poisson distributed with mean t. Remark. In [CFG01] the authors point out that defining quantum walks in continuous time allows unitarity without having to extend the graph with a direction space and a chosen local operation. On the other hand, it is harder to see how to carry out such a walk in a generically programmable way using only local ....
Andrew Childs, Edward Farhi, and Sam Gutmann. An example of the difference between quantum and classical random walks. Los Alamos preprint archive, quant-ph/0103020, 2001.
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