Quantum walks in higher dimensions

T. D. Mackay; S. D. Bartlett; L. T. Stephenson; B. C. Sanders

doi:10.1088/0305-4470/35/12/304

Quantum walks in higher dimensions

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, B. C. Sanders

Research output: Contribution to journal › Article › peer-review

203 Citations (Scopus)

Abstract

We analyse the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the 'quantum coin toss' in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.

Original language	English
Pages (from-to)	2745-2753
Number of pages	9
Journal	Journal of physics A : mathematical and general
Volume	35
Issue number	12
DOIs	https://doi.org/10.1088/0305-4470/35/12/304
Publication status	Published - 2002

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title = "Quantum walks in higher dimensions",

abstract = "We analyse the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the 'quantum coin toss' in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.",

author = "Mackay, {T. D.} and Bartlett, {S. D.} and Stephenson, {L. T.} and Sanders, {B. C.}",

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AU - Bartlett, S. D.

AU - Stephenson, L. T.

AU - Sanders, B. C.

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Y1 - 2002

N2 - We analyse the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the 'quantum coin toss' in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.

AB - We analyse the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the 'quantum coin toss' in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.

U2 - 10.1088/0305-4470/35/12/304

DO - 10.1088/0305-4470/35/12/304

M3 - Article

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VL - 35

SP - 2745

EP - 2753

JO - Journal of physics A : mathematical and general

JF - Journal of physics A : mathematical and general

IS - 12

ER -

Quantum walks in higher dimensions

Abstract

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