The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases

We propose an extension to the Pauli stabiliser formalism that includes fractional 2π/N rotations around xmlns:mml="http://www.w3.org/1998/Math/MathML">Z axis for some integer xmlns:mml="http://www.w3.org/1998/Math/MathML">N. The resulting generalised – denoted XP allows a wider range of states and codespaces be represented. describe which arise in formalism, demonstrate equivalence between 'weighted hypergraph states' generalisation both weighted graph states. Given arbitrary set operators, we present algorithms determining codespace logical operators code. Finally, consider whether measurements on codes can classically simulated.