2014/01/31 by B. Kollár, Bálint Kollár, Jaroslav Novotný +3
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Continuum percolation theory #Discrete mathematics #Graph #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum mechanics #Quantum walk #Quantum-Dot Cellular Automata #Random graph #Random walk #Statistical physics #Topology (electrical circuits) #Unitary state #quant-ph
paper · pdf · doi:10.1088/1367-2630/16/2/023002
published as New J. Phys. 16, 023002 (2014) · 21 pages, 3 figures
openalex publication_date 2014/02/04 · arxiv created 2014/02/11 · arxiv updated 2014/02/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on two-dimensional finite integer lattices with percolation. Based on this theory, we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking.