PlanetPhysics/Quantum Nano Automata

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).

A quantum nano-automaton ({\mathbf nanorobot, or nanocomputer}) is precisely defined mathematically as a Quantum Algebraic Topology object determined by the quantum triplet  $$(\grp,H -\Re_{\grp}, Aut(\grp)$$), where $$\grp$$ is a locally compact quantum groupoid, H -$$\Re_{\grp}$$ are the unitary (GNS) representations of $$\grp$$ on rigged Hilbert spaces $$\Re_\grp$$ of quantum states and quantum operators on Hilbert spaces H , and $$Aut(\grp)$$ 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