# 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* **Failed to parse (unknown function "\grp"): {\displaystyle (\grp,''H'' -\Re_{\grp}, Aut(\grp)}**
), where **Failed to parse (unknown function "\grp"): {\displaystyle \grp}**
is a locally compact *quantum groupoid* , *H* -**Failed to parse (unknown function "\grp"): {\displaystyle \Re_{\grp}}**
are the unitary (GNS) representations of **Failed to parse (unknown function "\grp"): {\displaystyle \grp}**
on rigged Hilbert spaces **Failed to parse (unknown function "\grp"): {\displaystyle \Re_\grp}**
of quantum states and quantum operators on Hilbert spaces *H* , and **Failed to parse (unknown function "\grp"): {\displaystyle 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