The paper presents a novel approach to solving eigenvalue problems on a photonic quantum processor, which significantly reduces the requirements for coherent evolution compared to traditional methods. The authors introduce a variational eigenvalue solver (QVE) that combines a highly reconfigurable photonic quantum processor with a classical optimization algorithm. This method is demonstrated experimentally by calculating the ground-state molecular energy of He-H⁺, a problem in quantum chemistry. The QVE algorithm efficiently computes the expectation value of a Hamiltonian using local measurements, reducing the coherence time requirements and making more efficient use of quantum resources. The approach is shown to be feasible and potentially useful for solving large-scale eigenvalue problems in various fields, including chemistry, internet search engines, and material design. The experimental setup uses integrated photonics technology and a spontaneous parametric downconversion single-photon source, combined with a classical CPU for optimization. The results demonstrate the ability to prepare non-separable states and produce entangled states, which are crucial for accurate descriptions of general quantum systems. The bond dissociation curve of He-H⁺ is calculated, with the experimental data closely matching the theoretical values, validating the effectiveness of the proposed method.The paper presents a novel approach to solving eigenvalue problems on a photonic quantum processor, which significantly reduces the requirements for coherent evolution compared to traditional methods. The authors introduce a variational eigenvalue solver (QVE) that combines a highly reconfigurable photonic quantum processor with a classical optimization algorithm. This method is demonstrated experimentally by calculating the ground-state molecular energy of He-H⁺, a problem in quantum chemistry. The QVE algorithm efficiently computes the expectation value of a Hamiltonian using local measurements, reducing the coherence time requirements and making more efficient use of quantum resources. The approach is shown to be feasible and potentially useful for solving large-scale eigenvalue problems in various fields, including chemistry, internet search engines, and material design. The experimental setup uses integrated photonics technology and a spontaneous parametric downconversion single-photon source, combined with a classical CPU for optimization. The results demonstrate the ability to prepare non-separable states and produce entangled states, which are crucial for accurate descriptions of general quantum systems. The bond dissociation curve of He-H⁺ is calculated, with the experimental data closely matching the theoretical values, validating the effectiveness of the proposed method.