  Quantum algorithms often assume independent spin qubits to produce trivial
$|\uparrow\rangle=|0\rangle$, $|\downarrow\rangle=|1\rangle$ mappings. This can
be unrealistic in many solid-state implementations with sizeable magnetic
interactions. Here we show that the lower part of the spectrum of a molecule
containing three exchange-coupled metal ions with $S=1/2$ and $I=1/2$ is
equivalent to nine electron-nuclear qubits. We derive the relation between spin
states and qubit states in reasonable parameter ranges for the rare earth
$^{159}$Tb$^{3+}$ and for the transition metal Cu$^{2+}$, and study the
possibility to implement Shor's Quantum Error Correction code on such a
molecule. We also discuss recently developed molecular systems that could be
adequate from an experimental point of view.

Quantum Physics