Fig. 4: Entangled state of anyon-encoded logical qubits by means of braiding.

a, Logical operators of the three logical qubits encoded in the eight anyons (other basis choices are possible). The coloured curves in the left column denote plaquette violation paths, before reduction to shorter, equivalent Pauli strings measured in the experiment (right column). b, Worldline schematic of the single exchange used to realize an entangled state of the logical qubits. c, Single exchange of the non-Abelian anyons, showing measurements of the stabilizers throughout the protocol. Yellow triangles represent the locations of the σ, whereas brown and green lines denote their paths. The average stabilizer values are 0.95 ± 0.04 and 0.88 ± 0.05 (one standard deviation) in the first and last step, respectively. Each stabilizer was measured n = 20,000 times in each step. d,e, Real (d) and imaginary (e) parts of the reconstructed density matrix from the quantum state tomography. \({\rm{Re}}(\rho )\) has clear peaks in its corners, as expected for a GHZ state on the form \((\left|000\right\rangle +\left|111\right\rangle )/\sqrt{2}\). The overlap with the ideal GHZ state is \({\rm{Tr}}\{\,{\rho }_{{\rm{GHZ}}}\rho \}=0.623\pm 0.004\), where the uncertainty is one standard deviation determined from bootstrapping.