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].

@ __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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