  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.
