We experimentally demonstrate a qubit-efficient variational quantum eigensolver(VQE) algorithm using a superconducting quantum processor,employing minimal quantum resources with only a transmon qubit coupled to a high-coherence photonic qubit.By leveraging matrix product states to compress the quantum state representation,we simulate an N+1-spin circular Ising model with a transverse field.Furthermore,we develop an analog error mitigation approach through zero-noise extrapolation by introducing a precise noise injection technique for the transmon qubit.As a validation,we apply our error-mitigated qubit-efficient VQE in determining the ground state energies of a 4-spin Ising model.Our results demonstrate the feasibility of performing quantum algorithms with minimal quantum resources while effectively mitigating the impact of noise,offering a promising pathway to bridge the gap between theoretical advances and practical implementations on current noisy intermediate-scale quantum devices.