Bad Qubits — Learn Quantum by Doing

Multiple choice

In the toric code, the electric charge e (a Z-string endpoint) and magnetic flux m (an X-string endpoint) are each individually bosons. What phase does the state acquire when an m is carried on a closed loop fully around a single e?

+i (a quarter-turn phase, theta = pi/2)
+1 (no phase, since both e and m are bosons)
-1 (mutual statistics phase e^{i*theta} with theta = pi), enforced by XZ = -ZX at the crossing
e^{i*pi/4} (the T-gate phase)