2014/04/17 by Pablo Arrighi, Stefano Facchini, Marcelo Forets · 47 citations
Computer Science · Mathematics · Physics and Astronomy · #Covariance #Covariant transformation #Lorentz covariance #Lorentz transformation #Mathematical physics #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum algorithm #Quantum and electron transport phenomena #Quantum cellular automaton #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.1088/1367-2630/16/9/093007
published in New Journal of Physics 16(9), 093007 (IOP Publishing) · 21 pages, 15 figures
arxiv created 2014/04/17 · openalex publication_date 2014/09/05 · arxiv updated 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We formalize a notion of discrete Lorentz transforms for quantum walks (QW) and quantum cellular automata (QCA), in -dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit equivalence rules. Within this framework, we show the first-order-only covariance of the Dirac QW. We then introduce the clock QW and the clock QCA, and prove that they are exactly discrete Lorentz covariant. The theory also allows for non-homogeneous Lorentz transforms, between non-inertial frames.