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.

@ __ General references__: Meyer JSP(96)qp, PLA(96)qp [no homogeneous, scalar, unitary ones on Euclidean lattices], qp/96;
Gudder IJTP(99)
[overview]; 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;
Wiesner a0808-en
[rev]; McDonald et al SPIE(12)-a1208 [geometric view]; 't Hooft a1405 [and quantum foundations]; 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].

@ __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 a1608.

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30 jan 2017