Figure 2

The Fibonacci Levin-Wen model is defined on a trivalent lattice. Each edge hosts a spin-\(1/2\) particle (a so-called data qubit) depicted here by a black dot. (a) Vertex v where three edges of the lattice meet. The state of the three qubits at the vertex v is \(| ijk\rangle\). (b) Twelve data qubits (black dots) needed to define the plaquette operator \(B_{p}\) on the trivalent lattice. In order to perform non-demolition measurements of vertex and plaquette operators, one introduces ancillary qubits (green squares). Here \(\alpha_{0}\) is used to measure \(B_{p}\), while the remaining ancillary qubits \(\alpha _{1-6}\) are used to measure the six vertex operators. This number of additional qubits is appropriate for the plaquette reduction method of Ref. [9].