Over the past several decades, topology has played a pivotal role in physics research. In particular, the quantum geometric tensor, which provides local information about topological properties, has garnered widespread attention. It can reveal a number of intriguing topological properties, yet it had never been measured in non-Abelian systems prior to this study. Herein, we utilize a four-qubit quantum system in a superconducting circuit to construct a degenerate Hamiltonian with parameter modulation. By applying periodic driving to the Hamiltonian, we simulate the Bernevig-Hughes-Zhang (BHZ) model and obtain the quantum geometric tensor via interference oscillations. Furthermore, we reveal its topological characteristics by extracting topological invariants, demonstrating an effective protocol for the quantum simulation of non-Abelian systems.
