Mimicking the probability distribution of a two-dimensional grover walk with a single-qubit coin
Di Franco, C.
Mc Gettrick, M.
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Di Franco, C. Mc Gettrick, M.; Busch, Th. (2011). Mimicking the probability distribution of a two-dimensional grover walk with a single-qubit coin. Physical Review Letters 106 (8),
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.