  We construct quantum error-correcting codes that embed a finite-dimensional
code space in the infinite-dimensional Hilbert state space of rotational states
of a rigid body. These codes, which protect against both drift in the body's
orientation and small changes in its angular momentum, may be well suited for
robust storage and coherent processing of quantum information using rotational
states of a polyatomic molecule. Extensions of such codes to rigid bodies with
a symmetry axis are compatible with rotational states of diatomic molecules, as
well as nuclear states of molecules and atoms. We also describe codes
associated with general nonabelian compact Lie groups and develop orthogonality
relations for coset spaces, laying the groundwork for quantum information
processing with exotic configuration spaces.
