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arXiv · 1010.2470

Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin

C. Di Franco·M. McGettrick·Th. Busch
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Abstract

Multi-dimensional quantum walks usually require large coin spaces. Here we show that the non-localized case of the spatial density probability of the two-dimensional Grover walk can be obtained using only a two-dimensional coin space and a quantum walk in alternate directions. We present a formal proof of this correspondence and analyze the behavior of the coin-position entanglement as well as the x-y spatial entanglement in our scheme with respect to the Grover one. We show that our experimentally simpler scheme allows to entangle the two orthogonal directions of the walk more efficiently.

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C. Di Franco, M. McGettrick, Th. Busch. 2011-02-24. Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin. https://doi.org/10.1103/physrevlett.106.080502

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