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

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

Di Franco, Carlo; Mc Gettrick, M.; Busch, Thomas
Date: 2011
Copyright: © 2011, American Physical Society
Related: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.080502
Citation: Di Franco, C., Mc Gettrick, M. and Busch, T. (2011) 'Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin', Physical Review Letters, 106(8), 080502 (4pp). doi: 10.1103/PhysRevLett.106.080502
Published Version: 10.1103/PhysRevLett.106.080502

Abstract:

The nonlocalized 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. This significantly reduces the resources necessary for its feasible experimental realization. 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. Our scheme allows us to entangle the two orthogonal directions of the walk more efficiently.

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