PlanetPhysics/Quantum Nano Automata

Description: A quantum [[../QuantumComputers/|nano-automaton]] or (quantum nano-computer) is realized as a microphysical nano-device represented by a [[../LQG2/|quantum automaton]] that is also capable of quantum [[../LQG2/|computation]] involving, for example, a [[../CosmologicalConstant2/|field]] of computations specified over a [[../WeakHopfAlgebra/|quantum groupoid]]. The latter can be realized as a locally compact ([[../CoIntersections/|topological]]) [[../LocallyCompactGroupoid/|groupoid]], topological semi-group; in the more general case, it can be defined over a quantum [[../CategoryOfLogicAlgebras/|algebraic category]], [[../DoubleQuantumAlgebroid/|quantum algebroid]] or a higher dimensional [[../TrivialGroupoid/|algebraic structure]] (as previously defined in [[../HigherDimensionalAlgebra2/|higher dimensional algebra]]).

A quantum nano-automaton ({\mathbf nanorobot, or nanocomputer}) is precisely defined mathematically as a [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]] [[../TrivialGroupoid/|object]] determined by the quantum triplet Failed to parse (unknown function "\grp"): {\displaystyle (\grp,''H'' -\Re_{\grp}, Aut(\grp)} ), where Failed to parse (unknown function "\grp"): {\displaystyle \grp} is a locally compact quantum groupoid , H -Failed to parse (unknown function "\grp"): {\displaystyle \Re_{\grp}} are the unitary (GNS) [[../CategoricalGroupRepresentation/|representations]] of Failed to parse (unknown function "\grp"): {\displaystyle \grp} on [[../I3/|rigged Hilbert spaces]] Failed to parse (unknown function "\grp"): {\displaystyle \Re_\grp} of quantum states and [[../QuantumOperatorAlgebra5/|quantum operators]] on [[../NormInducedByInnerProduct/|Hilbert spaces]] H , and Failed to parse (unknown function "\grp"): {\displaystyle Aut(\grp)} is the transformation, or automorphism, groupoid of quantum transitions.

Note: Quantum nano-automata possess intrinsic, [[../ExtendedQuantumSymmetries/|extended quantum symmetries]] defined by quantum groupoid or quantum algebroid representations