We report an experimental work on simulating the Kitaev chain of one-dimensional $p$-wave superconductivity with long-range coupling using superconducting quantum circuits. The effective Hamiltonian of this model in the momentum space is mapped onto that of a qubit driven by a tunable microwave control field. By monitoring the dynamics of the qubit, we generate intuitive yet precise visualization of topological characteristics of different quantum phases of the system. Topological invariants can be directly deduced from the experimental results, without relying on indirect extraction from measurements such as microwave spectroscopy and temporal averaging. Therefore a much enhanced efficiency of measurement can be realized compared to other methods that are often used to simulate topological phase transitions. As a consequence, a comprehensive phase diagram covering a wide range of the parameter space is obtained. Topological phase transitions and quantum multicritical points are clearly demonstrated. In particular, new topological phases emerge as a consequence of long-range coupling. The method used here can be readily generalized to simulate more complex systems on different experimental platforms.

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