Cellular Automata  

In General > s.a. computation; game theory [life]; Order; quantum computation.
* Idea: A cellular automaton is a discrete model consisting of a regular grid of cells, each in one of a finite number of states and with a set of neighborhood cells, whose state is used in the rule for generating a new state for the specified cell.
* History: The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann, used in the 1970s by John Conway in his Game of Life, a 2D cellular automaton, and systematically studied starting in the 1980s with Stephen Wolfram's work.
@ General references: Wolfram CMP(84), 86; García-Morales a1203 [equivalence classes of CA rules, and complexity], a1605 [diagrammatic approach].
@ Related topics: Tisseur Nonlin(00)m.DS/03 [Lyapunov exponents, entropy]; Alonso-Sanz PhyA(05) [with memory, phase transitions]; 't Hooft FP(13)-a1205 [deterministic and 2D bosonic quantum field theory]; Elze PRA(14)-a1312-conf [action principle].
> Online resources: see Wikipedia page.

Quantum Cellular Automata > s.a. dirac equation.
@ Reviews: Gudder IJTP(99); Wiesner a0808-en; Arrighi a1904.
@ General references: Meyer JSP(96)qp, PLA(96)qp [no homogeneous, scalar, unitary ones on Euclidean lattices], qp/96; Svozil qp/02-conf [as models]; Andrecut & Ali PLA(04) [entanglement dynamics]; Schumacher & Werner qp/04 [reversible]; Pérez-Delgado & Cheung qp/05, PRA(07)-a0709; McDonald et al SPIE(12)-a1208 [geometric view]; D'Ariano et al PLA(14) [discrete path-integral formulation]; Pérez PRA(16)-a1504 [Dirac quantum cellular automaton]; Meyer & Shakeel PRA(16)-a1506 [without particle interpretation]; Elze JPCS(16)-a1604; Arrighi et al PRA(17) [quantum speedup in signaling]; Freedman & Hastings a1902 [classification]; Shah & Gorard a1910 [new formalism, and quantum complexity].
@ And quantum foundations: 't Hooft a1405 [cellular automaton interpretation of quantum mechanics]; Elze IJQI(17)-a1711, a1802-in [ontological states].
@ And quantum field theory: Svozil PLA(86); McGuigan qp/03 [lattice field theory]; Bisio et al AP(15)-a1412; Bisio et al PRA(16)-a1503 [3D, Lorentz symmetry]; Bisio et al FP(15)-a1601, FP(15)-a1601 [and quantum field theory]; D'Ariano & Perinotti FrPh(17)-a1608.

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