Quantum walks in higher dimensions

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

    Research output: Contribution to journalArticlepeer-review

    188 Citations (Scopus)


    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 languageEnglish
    Pages (from-to)2745-2753
    Number of pages9
    JournalJournal of physics A : mathematical and general
    Issue number12
    Publication statusPublished - 2002


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