Two examples of discrete-time quantum walks taking continuous steps

Details Two examples of discrete-time quantum walks taking continuous steps Two examples of discrete-time quantum walks taking continuous steps

2003-10-04

arxiv.org/abs/quant-ph/0310026v2

Physics

Quantum Physics

6 pages. Title changed and more content added

Scientific paper

This note introduces some examples of quantum random walks in d-dimensional Eucilidean space and proves the weak convergence of their rescaled n-step densities. One of the examples is called the Plancherel quantum walk because the "quantum coin flip" is the Fourier Integral (or Plancherel) Transform. The other examples are the Birkhoff quantum walks, so named because the coin flips are effected by means of measure preserving transformations to which the Birkhoff's Ergodic Theorem is applied.

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