Fig. 4: Braiding statistics.
From: Non-Abelian braiding of Fibonacci anyons with a superconducting processor
a, Creation and fusion of Fibonacci anyons, which can be described by the world lines (top), with time flowing from down to up. The corresponding operations in the string-net picture are shown in the bottom panel, where two pairs of Fibonacci anyons can be created and fused with two F moves and their inverses, respectively. The four anyons are labelled as τ1,2,3,4 and the fan sectors sketch the original hexagon plaquettes. b, World-line representation and the corresponding string-net picture for the two braiding operations σ1 (up) and σ2 (down). We use R moves to transfer the anyons across different plaquettes, and F moves to move them along the edge (right panel). c,d, 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 σ2 by applying σ1σ2 on the ground state (iii), which is verified by the similar fusion results observed after applying σ2σ1σ2 on the ground state (iv). In addition, we can also extract the monodromy matrix by applying σ2σ2 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).
