2009/02/20 by Domenico D'Alessandro, Domenico D’Alessandro
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Connection (principal bundle) #Discrete mathematics #Discrete time and continuous time #Geometry #Graph #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum graph #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1016/s0034-4877(10)80025-4
arxiv created 2009/02/20 · openalex publication_date 2010/08/01 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
I obtain the dynamics of the continuous time quantum walk on a d-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main result of arXiv:quant-ph/0606050 which proved this limit for the infinite line. By highlighting the main features of the limiting procedure, I then extend it to general graphs. For a given discrete time quantum walk on a general graph, I single out the type of continuous dynamics (Hamiltonians) that can be obtained as a limit of the discrete time dynamics.