Variational quantum eigensolver (VQE) is promising to show quantum advantage on near-term noisy-intermediate-scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially the physical noise on realistic quantum computers. We study systematically the effect of noise for the VQE algorithm, by performing numerical simulations with various local noise models, including the amplitude damping, dephasing, and depolarizing noise. We show that the ground state energy will deviate from the exact value as the noise probability increase and normally noise will accumulate as the circuit depth increase. We build a noise model to capture the noise in a real quantum computer. Our numerical simulation is consistent with the quantum experiment results on IBM Quantum computers through Cloud. Our work sheds new light on the practical research of noisy VQE. The deep understanding of the noise effect of VQE may help to develop quantum error mitigation techniques on near team quantum computers.
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