2006/06/20 by Paweł Kurzyński, Pawel Kurzynski
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Dirac (video compression format) #Dirac equation #Discretization #Klein–Gordon equation #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum dynamics #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #Relativistic quantum mechanics #Relativistic wave equations #Two-body Dirac equations #Zitterbewegung #quant-ph
paper · pdf · doi:10.1016/j.physleta.2008.08.017
published as Phys. Lett. A 372, 6125 (2008) · 4 pages, 3 figures
arxiv created 2006/06/20 · openalex publication_date 2008/08/14 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum walks are not only algorithmic tools for quantum computation but also not trivial models which describe various physical processes. The paper compares one-dimensional version of the free particle Dirac equation with discrete time quantum walk (DTQW). We show that the discretized Dirac equation when compared with DTQW results in interesting relations. It is also shown that two relativistic effects associated with the Dirac equation, namely Zitterbewegung (quivering motion) and Klein's paradox, are present in DTQW, which can be implemented within non-relativistic quantum mechanics.