This paper details the use of a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrates braiding of Fibonacci anyons with universal computational power. The non-trivial topological nature of the quantum states is demonstrated by measuring topological entanglement entropy. The fusion rule and non-Abelian braiding statistics of two pairs of Fibonacci anyons are demonstrated through unitary gate application on the underlying physical qubits. The results establish a digital approach for exploring non-Abelian topological states and their braiding statistics using current noisy intermediate-scale quantum processors.
