  This study introduces a systematic approach for analyzing strongly correlated
systems by adapting the conventional quantum cluster method to a quantum
circuit model. We have developed a more concise formula for calculating the
cluster's Green's function, requiring only real-number computations on the
quantum circuit instead of complex ones. This approach is inherently more
suited to quantum circuits, which primarily yield statistical probabilities. As
an illustrative example, we explored the Hubbard model on a 2D lattice. The
ground state is determined utilizing Xiaohong, a superconducting quantum
processor equipped with 66 qubits, supplied by QuantumCTek Co., Ltd.
Subsequently, we employed the circuit model to compute the real-time retarded
Green's function for the cluster, which is then used to determine the lattice
Green's function. We conducted an examination of the band structure in the
insulator phase of the lattice system. This preliminary investigation lays the
groundwork for exploring a wealth of innovative physics within the field of
condensed matter physics.
