Fig. 1: Fibonacci anyon and string-net model.
From: Non-Abelian braiding of Fibonacci anyons with a superconducting processor
a, World line of braiding Fibonacci anyons. We create two pairs of Fibonacci anyons from vacuum, braid the middle two and then fuse them. In terms of topological quantum computing, such a braid will transfer the initial logical state \(\left\vert \bar{0}\right\rangle\) to the logical state \({\left\vert \varPsi \right\rangle }_{{\rm{L}}}={\phi }^{-1}{{\rm{e}}}^{4\uppi{\rm{i}}/5}\left\vert \bar{0}\right\rangle +{\phi }^{-1/2}{{\rm{e}}}^{-3\uppi{\rm{i}}/5}\left\vert \bar{1}\right\rangle\), which can be detected by measuring the fusion results of the two pairs of anyons. b, Fibonacci string-net model is defined on a honeycomb lattice, which, in turn, is constructed out of the underlying square lattice that depicts the geometry for the transmon qubits of our quantum processor. The Qv and Bp operators are three- and twelve-body projectors acting on the qubits associated with each vertex and plaquette, as highlighted in olive and blue, respectively. A pair of Fibonacci anyons can be created at the endpoints (red dots) of an open string operator (coral line), which can be extended and turned around by F and R moves. c, Effects of F move (up) and R move (down). The F-move (R-move) operator acts on five (three) qubits circled by the dashed lines, which extends (adjusts the direction of) the string operator and moves the Fibonacci anyon along (across) the plaquettes (Methods and Supplementary Section I.E).
