2003/10/04 by Alex D. Gottlieb, Gottlieb, Alex D.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0310026
6 pages. Title changed and more content added
openalex publication_date 2003/10/04 · arxiv created 2003/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.