  We propose an extension to the Pauli stabiliser formalism that includes
fractional $2\pi/N$ rotations around the $Z$ axis for some integer $N$. The
resulting generalised stabiliser formalism - denoted the XP stabiliser
formalism - allows for a wider range of states and codespaces to be
represented. We describe the states which arise in the formalism, and
demonstrate an equivalence between XP stabiliser states and 'weighted
hypergraph states' - a generalisation of both hypergraph and weighted graph
states. Given an arbitrary set of XP operators, we present algorithms for
determining the codespace and logical operators for an XP code. Finally, we
consider whether measurements of XP operators on XP codes can be classically
simulated.
