The anyonic mutual statistics of the quasiparticles demonstrate the logical operations performed by topologically non-trivial loops. Consider the creation of a pair of e anyons followed by the transport of one around a topologically nontrivial loop, such as that shown on the torus in blue on the figure above, before the pair are reannhilated. The state is returned to the stabilizer space, but the loop implements a logical operation on one of the stored qubits. If m anyons are similarly moved through the red loop above a logical operation will also result. The phase of − − 1 resulting when braiding the anyons shows that these operations do not commute, but rather anticommute. They may therefore be interpreted as logical Z and X Pauli operators on one of the stored qubits. The corresponding logical Pauli's on the other qubit correspond to an m anyon following the blue loop and an e anyon following the red. No braiding occurs when e and m pass through parallel paths, the phase of − − 1 therefore does not arise and the corresponding logical operations commute. This is as should be expected since these form operations acting on different qubits.