Talk:PlanetPhysics/Quantum Nano Automata

Original TeX Content from PlanetPhysics Archive

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\begin{document}

 \textbf{Description:} A \emph{quantum \htmladdnormallink{nano-automaton}{http://planetphysics.us/encyclopedia/QuantumComputers.html}} or \emph{(quantum nano-computer)}
is realized as a microphysical nano-device represented by a \htmladdnormallink{quantum automaton}{http://planetphysics.us/encyclopedia/LQG2.html} that is also capable of quantum \htmladdnormallink{computation}{http://planetphysics.us/encyclopedia/LQG2.html} involving, for example, a \htmladdnormallink{field}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} of computations specified over a \htmladdnormallink{quantum groupoid}{http://planetphysics.us/encyclopedia/WeakHopfAlgebra.html}.
The latter can be realized as a locally compact (\htmladdnormallink{topological}{http://planetphysics.us/encyclopedia/CoIntersections.html}) \htmladdnormallink{groupoid}{http://planetphysics.us/encyclopedia/LocallyCompactGroupoid.html}, topological semi-group; in the more general
case, it can be defined over a \emph{quantum \htmladdnormallink{algebraic category}{http://planetphysics.us/encyclopedia/CategoryOfLogicAlgebras.html}}, \htmladdnormallink{quantum algebroid}{http://planetphysics.us/encyclopedia/DoubleQuantumAlgebroid.html} or a higher dimensional \htmladdnormallink{algebraic structure}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} (as previously defined in \htmladdnormallink{higher dimensional algebra}{http://planetphysics.us/encyclopedia/HigherDimensionalAlgebra2.html}).

\begin{definition}
A \emph{quantum nano-automaton} ({\bf nanorobot, or nanocomputer}) is precisely defined mathematically as a \htmladdnormallink{Quantum Algebraic Topology}{http://planetphysics.us/encyclopedia/TriangulationMethodsForQuantizedSpacetimes2.html} \htmladdnormallink{object}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} determined by the \emph{quantum triplet} $(\grp,\emph{H}-\Re_{\grp}, Aut(\grp)$), where $\grp$ is a locally compact \emph{quantum groupoid}, \emph{H}-$\Re_{\grp}$ are the unitary (GNS) \htmladdnormallink{representations}{http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of $\grp$ on \htmladdnormallink{rigged Hilbert spaces}{http://planetphysics.us/encyclopedia/I3.html} $\Re_\grp$ of quantum states and \htmladdnormallink{quantum operators}{http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra5.html} on \htmladdnormallink{Hilbert spaces}{http://planetphysics.us/encyclopedia/NormInducedByInnerProduct.html} \emph{H}, and $Aut(\grp)$ is the transformation, or automorphism, groupoid of quantum transitions.
\end{definition}



\textbf{Note:} Quantum nano-automata possess intrinsic, \htmladdnormallink{extended quantum symmetries}{http://planetphysics.us/encyclopedia/ExtendedQuantumSymmetries.html} defined by quantum groupoid or quantum algebroid representations

\end{document}