Fig. 5: Entanglement transfer from anyons to CC defects for initializing topological qutrits.

a A sketch of the different steps, with intermediate states, involved in moving a charge anyon around defects. The braiding followed by measuring an ancilla transfers a Bell state of charge anyons into an entangled logical state of CC defects. b Results for the final step as depicted in (a). We create \({{\mathbb{Z}}}_{3}\) ground state with two pairs of defects, labeled 1 and 2 (cf. Supplementary Fig. 10). Defect pair 1, marked with the  × -hatch pattern, extends between points B₀ and A₇. Defect pair 2, indicated by the /-hatch pattern, has endpoints B₁ and A₈. The orange loop represents a braid that stabilizes the prepared topological qutrit state; a black border on the solid circle indicates the application of \({{\mathcal{X}}}^{\dagger }\), while its absence indicates \({\mathcal{X}}\). The expectation values of the projectors \({\Pi }_{{B}_{0}}^{1}\) and \({\Pi }_{{B}_{1}}^{1}\) for the non-local stabilizers are 0.931(15) and 0.927(15), respectively. We measure the expectation values of \({\Pi }_{{A}_{7}}^{1}\), \({\Pi }_{{A}_{8}}^{1}\), and \({\Pi }_{{A}_{7}{A}_{8}}^{1}\) for different ancilla outcomes (\(\left\vert {0}_{a}\right\rangle \), \(\left\vert {1}_{a}\right\rangle \), and \(\left\vert {2}_{a}\right\rangle \)). For \({\Pi }_{{A}_{7}}^{1}\), the measured values are 0.44(5), 0.40(5), and 0.39(5), respectively. Similarly, for \({\Pi }_{{A}_{8}}^{1}\), the values are 0.44(5), 0.42(5), and 0.36(5). Finally, \({\Pi }_{{A}_{7}{A}_{8}}^{1}\) yields values of 0.81(4), 0.78(4), and 0.74(4) for the respective ancilla states. This is a manifestation of the fact that, although the outcomes for each individual defect pair are random, they are jointly in an entangled state.