Extended Data Fig. 9: Alternative protocol for braiding σ.

a, Schematic displaying the braiding process of the two σ-pairs. b, Experimental demonstration of braiding, displaying the values of the stabilizers throughout the process. Two σ-pairs, A and B, are created from the vacuum \({\mathbb{1}}\), and one of the D3Vs in pair A is brought to the right side of the grid. Next, a σ from pair B is moved to the top, thus crossing the path of the first σ, before bringing the σ from pair A back again to complete the braid. The diagonal σ move performed in step VI is achieved by including two SWAP-gates, corresponding to 6 additional CZ-gates. The yellow triangles represent the locations of the σ, while the brown and green lines represent the paths of σ from pair A and B, respectively. The average absolute stabilizer value is 0.93 ± 0.06 and 0.77 ± 0.09 in the first and last step, respectively. c, After braiding the σ, we search for hidden fermions by measuring the Pauli string \(\hat{{\mathcal{P}}}\) (left panels), which here is equivalent to \(\hat{Y}\) on the qubit where the two σ overlap. The measurement yields \(\langle \hat{{\mathcal{P}}}\rangle =\langle \hat{Y}\rangle =-\,0.71\,\pm \,0.01\), indicating creation of a fermion. Right: world-lines of braiding process, including non-local measurement based on plaquette violation loop. d, Same as c, but after braiding two distinguishable σ, achieved by applying the inverse two-qubit gates when moving the σ in pair B. The measurement yields \(\langle \hat{Y}\rangle =+\,0.71\,\pm \,0.01\), indicating no fermion creation.