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).

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 $ (\mathsf{G},\emph{H}-\Re_{\mathsf{G}}, Aut(\mathsf{G})$ ), where $ \mathsf{G}$ is a locally compact quantum groupoid, H- $ \Re_{\mathsf{G}}$ are the unitary (GNS) representations of $ \mathsf{G}$ on rigged Hilbert spaces $ \Re_\mathsf{G}$ of quantum states and quantum operators on Hilbert spaces H, and $ Aut(\mathsf{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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