Connecting the discrete and continuous-time quantum walks

Details Connecting the discrete and continuous-time quantum walks Connecting the discrete and continuous-time quantum walks

2006-06-06

arxiv.org/abs/quant-ph/0606050v1

Phys. Rev. A 74, 030301 (R) (2006)

Physics

Quantum Physics

5 pages, 1 figure

Scientific paper

10.1103/PhysRevA.74.030301

Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time quantum walk. Though the properties of these two walks have shown similarities, it has remained an open problem to find the exact relation between the two. The precise connection of these two processes, both quantally and classically, is presented. Extension to higher dimensions is also discussed.

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