We select two periodic systems with different level of complexity for these calculations. One of them is the distorted hydrogen chain as an example of very simple systems, and the other one is iron crystal in the BCC and FCC phases as it is considered to be inaccessible by using classical computational wavefunction methods. The ground state energies are evaluated based on the translational quantum subspace expansion (TransQSE) method for the hydrogen chain, and periodic boundary condition adapted VQE for our iron models. In addition to the usual state preparation and measurement noise mitigation, we apply a novel noise mitigation technique, which performs post-selection of shot counts based on Z2 and U1 symmetry verification. By applying these techniques for the simplest 2 qubit iron model systems, the energies obtained by the hardware calculations agree with those of the state-vector simulations within ∼5 kJ/mol. Although the quantum computational resources used for those experiments are still limited, the systematic resource reduction applied to obtain our simplified models will give us a way to scale up by rolling approximations back as quantum hardware matures.