quantum nano-automataQuantumNanoAutomata2009-01-09 03:19:562009-01-09 03:22:25Topic\begin{definition}: alternatively, as a quantum algebraic topology object, a \emph{quantum automaton} is defined by the
triplet $(\grp,\emph{H}-\Re_{\grp}, Aut(\grp)$), where $\grp$ is a locally compact \emph{quantum groupoid},
\emph{H}-$\Re_{\grp}$ are the unitary representations of $\grp$ on rigged Hilbert spaces $\Re_\grp$ of quantum states and quantum operators on \emph{H}, and $Aut(\grp)$ is the transformation, or automorphism, groupoid of quantum transitions.
\end{definition}quantum nanoautomatonquantum nano-automata% this is the default PlanetPhysics preamble. as your knowledge
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% define commands here\textbf{Description:} A \emph{quantum nano-automaton} or \emph{(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 \emph{quantum algebraic category}, quantum algebroid or a higher dimensional algebraic structure (as previously defined in higher dimensional algebra).
\textbf{Note:} Quantum nano-automata possess intrinsic, extended quantum symmetries defined by quantum groupoid or quantum algebroid representations