Surface code on a chain of spheres
= Surface code on a chain of spheres
Join $n$ spheres pole to pole and draw $m$ longitude edges on each sphere. Qubits on edges, two-edge face $Z$ stabilizers, and vertex $X$ stabilizers realize the concatenated phase-and-bit-flip repetition code. A pole-to-pole path has weight $n$, while a dual equatorial cut has weight $m$.