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quantum nano-automata

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

Definition 0.1. A quantum nano-automaton (nanorobot, or nanocomputer) is precisely defined mathematically as a quantum algebraic topology object determined by the quantum triplet (G,H −ℜG,Aut(G)), where G is a locally compact quantum groupoid, H-ℜG are the unitary (GNS) representations of G on rigged Hilbert spaces ℜG of quantum states and quantum operators on Hilbert spaces H, and Aut(G) is the transformation, or automorphism, groupoid of quantum transitions.

Note: Quantum nano-automata possess intrinsic, extended quantum symmetries defined by quantum groupoid or quantum algebroid representations


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See Also: quantum automata, locally compact groupoid

Other names:  nanorobot, nanodevice
Also defines:  quantum nanoautomaton
Keywords:  quantum nano-automata

Cross-references: extended quantum symmetries, Hilbert spaces, quantum operators, rigged Hilbert spaces, representations, quantum algebraic topology, higher dimensional algebra, algebraic, quantum algebroid, algebraic category, groupoid, topological, quantum groupoid, computation, quantum automaton, nano-automaton
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This is version 13 of quantum nano-automata, born on 2009-01-09, modified 2009-02-13.
Object id is 358, canonical name is QuantumNanoAutomata.
Accessed 4147 times total.

Classification:
Physics Classification: 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )

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