This paper reports the experimental realization of non-Abelian topological order in the Fibonacci string-net model using a superconducting quantum processor. The Fibonacci anyons, which are quasiparticles in this model, exhibit non-Abelian braiding statistics and can be used for universal quantum computation. The researchers created two pairs of Fibonacci anyons and demonstrated their fusion rules and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. They also measured the topological entanglement entropy, which is a key indicator of topological order, and found that the prepared state has a large overlap with the ideal ground state of the Hamiltonian. The results show that the Fibonacci anyons created in the experiment are indeed Fibonacci anyons, as evidenced by the measured fusion results and the extracted monodromy matrix. The study demonstrates a versatile digital approach to exploring exotic non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors. The work provides strong evidence for the Fibonacci topological order of the ground state and highlights the potential of superconducting quantum processors for realizing topological quantum computation.This paper reports the experimental realization of non-Abelian topological order in the Fibonacci string-net model using a superconducting quantum processor. The Fibonacci anyons, which are quasiparticles in this model, exhibit non-Abelian braiding statistics and can be used for universal quantum computation. The researchers created two pairs of Fibonacci anyons and demonstrated their fusion rules and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. They also measured the topological entanglement entropy, which is a key indicator of topological order, and found that the prepared state has a large overlap with the ideal ground state of the Hamiltonian. The results show that the Fibonacci anyons created in the experiment are indeed Fibonacci anyons, as evidenced by the measured fusion results and the extracted monodromy matrix. The study demonstrates a versatile digital approach to exploring exotic non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors. The work provides strong evidence for the Fibonacci topological order of the ground state and highlights the potential of superconducting quantum processors for realizing topological quantum computation.