Convergence of coined quantum walks on d-dimensional Euclidean space
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Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and a translation conditional on the spin state. Coined quantum walks on the d-dimensional lattice can be treated as special cases of coined quantum walks on d-dimensional Euclidean space. We study quantum walks on d-dimensional Euclidean space and prove that the sequence of rescaled probability distributions in position space associated to the unitary evolution of the particle converges to a limit distribution.
11 pages
11 pages