Five braiding sequences ( c ) and the fusion results of Fibonacci anyon pairs at the end of each braiding ( d ). To demonstrate the braiding statistics, we create two pairs of Fibonacci anyons from vacuum, braid them along five different paths and then fuse them. Although the direct fusion of two anyon pairs right after their creation would lead the system back to vacuum (i), other braiding sequences will result in non-trivial fusion results ((ii)-(v)). In particular, we prepare the system into an eigenstate of 2 by applying 1 2 on the ground state (iii), which is verified by the similar fusion results observed after applying 2 1 2 on the ground state (iv). In addition, we can also extract the monodromy matrix by applying 2 2 and measuring the fusion result (v). The fusion results are obtained by measuring the two physical qubits ( Q (5,13) and Q (5,9) ; Extended Data Fig. 1 ) corresponding to the two string types (top-right corner in d ) ( Methods and Supplementary Section I.E ).
