The paper reports the experimental realization of non-Abelian topologically ordered states in the Fibonacci string-net model using a superconducting quantum processor. The authors demonstrate the creation, braiding, and fusion of Fibonacci anyons, which support universal topological quantum computation. They optimize the device fabrication and control processes to achieve high-fidelity quantum gates and prepare the desired non-Abelian ground state. The topological entanglement entropy is measured to characterize the topological order, and the braiding statistics of Fibonacci anyons are verified through braiding sequences. The results establish a versatile digital approach to exploring exotic non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.The paper reports the experimental realization of non-Abelian topologically ordered states in the Fibonacci string-net model using a superconducting quantum processor. The authors demonstrate the creation, braiding, and fusion of Fibonacci anyons, which support universal topological quantum computation. They optimize the device fabrication and control processes to achieve high-fidelity quantum gates and prepare the desired non-Abelian ground state. The topological entanglement entropy is measured to characterize the topological order, and the braiding statistics of Fibonacci anyons are verified through braiding sequences. The results establish a versatile digital approach to exploring exotic non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.