Fig. 3: Creation of and braiding around parafermion defects.

Any plaquette containing an anyon is colored black, with the value of \(\max ({{\Pi }_{\bullet }^{\omega }},{\Pi }_{\bullet }^{\bar{\omega }})\) displayed. An arrow within each plaquette indicates the direction specified by the arg 〈stabilizer〉, where the stabilizer could be A_p, B_p, or any of the defect stabilizers. The arrow’s direction serves as a visual cue to distinguish anyons from their conjugates. a, b A pair of defects is inserted into the ground state by measuring the middle qutrit in the \({\mathcal{X}}{\mathcal{Z}}\)-basis and performing feed-forward based on the measurement outcome. c A sketch illustrating the braiding experiment in steps (d–g). A pair of charges, e and \(\bar{e}\), is created by applying a \({\mathcal{Z}}\) operator, which toggles the eigenvalues of the neighboring green \(({\mathcal{X}})\)-type plaquettes. Charge \(\bar{e}\) remains fixed, while e is dragged through the defect pair and emerges as m on the other side of the defect pair, signaled by the fact a blue (\({\mathcal{Z}}\)-type) plaquette is now excited. The maximum estimation error is 0.022.