  Perturbation theory (PT) might be one of the most powerful and fruitful tools
for both physicists and chemists, which evoked an explosion of applications
with the blooming of atomic and subatomic physics. Even though PT is well-used
today, techniques for PT are significantly lacking in quantum computing. Here
we present a quantum circuit estimating both the energy and eigenstates
corrections with PT methods, which we claim is far superior to the classical
version when estimating the second order energy correction. Our approach is
further demonstrated with an application on the extended Hubbard model, where
numerical simulation based on qiskit is also presented. Unlike the popular
quantum variational circuit, there is no training or optimizing process in our
circuit, and all parameters are derived from the unperturbed Hamiltonian. Our
work offers a new approach to studying complex systems with quantum devices,
which might shed light on the quantum implementation of the more intricate
methods based on PT.
