quantum nano-automata | Physics Library

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 −ℜ_G,Aut(G)), where G is a locally compact quantum groupoid, H-ℜ_G are the unitary (GNS) representations of G on rigged Hilbert spaces ℜ_G 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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