Fig. 2: TC ingredients on the TTC boundary B.
The boundary checks Sj = Z2j−1Z2j (shown also as red segments) and perturbations X1 (blue dot) and X2jX2j+1 (blue segments) become \({\tau }_{j}^{z}{\tau }_{j+1}^{z}\) and \({\tau }_{l}^{x}\). The symmetry \({P}_{\tau }={\prod }_{j}{\tau }_{j}^{x}\) is a logical \(\overline{X}\) of the TO. Also shown is the assignment \({\tau }_{j+1}^{z}\) to \({{{\mathcal{Z}}}}_{{\gamma }_{Z}}\) with γZ ending on qubit 2j (dashed) or 2j + 1 (solid vertical line); the two choices differ by a deformation (cf. Fig. 1).
