<p>This paper constructs a quantum commons game model based on the homogeneous rational expectation theory and the Li–Du–Massar (LDM) quantization scheme and conducts a comparative analysis of its differences from the classical commons problem. Studies have found that within a specific range, the enhancement of quantum entanglement can expand the stable region of the system, increase the threshold of system bifurcation, and play a regulatory role in the complex dynamic behaviors of the model. When the farmers’ adjustment speed exceeds the critical threshold, the system will exhibit chaotic behavior accompanied by a bifurcation phenomenon. By introducing the delayed feedback control method, the chaotic behavior of the complex dynamic system can be redirected and stabilized at the quantum Nash equilibrium point. In addition, through numerical simulations, the correctness and effectiveness of the theoretical model are verified from the perspectives of the bifurcation diagram, the maximum Lyapunov exponent, and the strange attractor.</p>