Figure 7
From: Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
Graphical representation of encoding, storage and decoding procedure in subsystem surface code.
In the procedure Z-type errors happen with probability p, likewise errors on Xs stabilizer measurements performed between every horizontal plane. Horizontal links denote code qubits, vertical links are places to store the outcomes of syndrome measurements. Vertices in the lattice marked by red crosses correspond to nontrivial syndrome in the first horizontal slice k = 0 and changes of it in all subsequent k = 1, 2, …T slices. Both, top and bottom planes are divided into 3 parts: black, blue and green. For the latter one black qubit is prepared in |Ψin〉 state and blue (green) qubits in |+〉 (|0〉) states. The top plane illustrate decoding stage where syndromes are computed from single qubit measurements made in X eigenbasis. Three examples of actual error chains (elements of E) are represented by red thick lines. Each ends with a defect/defects (red crosses) or on a boundary (front wall or green regions). Corrections (Emin) are performed along the shortest paths due to a given metric and are represented by blue thick lines. Paths from E + Emin are either nontrivial or trivial chains, two examples of former and one of latter are shown in the picture. Nontrivial paths from E + Emin are dangerous since they change a parity of XL operator (see exclamation marks) and logical error may occur.
