  The variational quantum eigensolver (VQE) is one of the most appealing
quantum algorithms to simulate electronic structure properties of molecules on
near-term noisy intermediate-scale quantum devices. In this work, we generalize
the VQE algorithm for simulating extended systems. However, the numerical study
of an one-dimensional (1D) infinite hydrogen chain using existing VQE
algorithms shows a remarkable deviation of the ground state energy with respect
to the exact full configuration interaction (FCI) result. Here, we present two
schemes to improve the accuracy of quantum simulations for extended systems.
The first one is a modified VQE algorithm, which introduces an unitary
transformation of Hartree-Fock orbitals to avoid the complex Hamiltonian. The
second one is a Post-VQE approach combining VQE with the quantum subspace
expansion approach (VQE/QSE). Numerical benchmark calculations demonstrate that
both of two schemes provide an accurate enough description of the potential
energy curve of the 1D hydrogen chain. In addition, excited states computed
with the VQE/QSE approach also agree very well with FCI results.
