2021/07/26 by David Berenstein, Berenstein, David, Brian Kent +1
Computer Science · Physics and Astronomy · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Quantum many-body systems #Quantum-Dot Cellular Automata #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #hep-th #nlin.CG #quant-ph
paper · pdf · doi:10.48550/arxiv.2107.12191
4 pages, plus supplementary material. v2: references added
openalex publication_date 2021/07/26 · arxiv created 2021/08/24 · arxiv updated 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalized set of Clifford cellular automata, which includes all Clifford cellular automata, result from the quantization of a lattice system where on each site of the lattice one has a 2k-dimensional torus phase space. The dynamics is a linear map in the torus variables and it is also local: the evolution depends only on variables in some region around the original lattice site. Moreover it preserves the symplectic structure. These are classified by 2k× 2k matrices with entries in Laurent polynomials with integer coefficients in a set of additional formal variables. These can lead to fractal behavior in the evolution of the generators of the quantum algebra. Fractal behavior leads to non-trivial Lyapunov exponents of the original linear dynamical system. The proof uses Fourier analysis on the characteristic polynomial of these matrices.