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 ), where is a locally compact quantum groupoid, H- are the unitary (GNS) representations of on rigged Hilbert spaces of quantum states and quantum operators on Hilbert spaces H, and 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