A general scheme to perform quantum simulations with for plane-wave and Wannier function based methods

In the field of condensed matter chemistry, describing the hydrogen diffusion in materials remains a significant challenge.A precise computational characterization of electronic structures is essential to deepen our understanding of this process. Solving the Schrödinger equation to obtain ground-state properties presents exponential scaling challenges. Density Functional Theory (DFT) makes more feasible electronic structure calculations for many-body systems but it struggles with strongly correlated systems. Recent advancements in quantum computing offer potential solutions to overcome exponential scaling barriers. Despite progress, current quantum algorithms often exceed the capabilities of modern hardware, with deep circuits leading to errors and optimization challenges in large-scale problems. An alternative is to use hybrid quantum-classical algorithms which are based on the main advantages of both quantum and classical simulations to offset their weaknesses. Thus, we present an interface between Quantum ESPRESSO and Qiskit. Our workflow is a three steps method. The electronic structure of the crystal system is obtained by the use of the plane-wave based DFT software, Quantum ESPRESSO. We define an active space with the Kohn-Sham orbitals, calculate the one-electron and two-electron integrals for the active space, while the remaining electrons are approximated through the frozen core approximation. The ground-state Hamiltonian, built from the one and two-electron integrals, is then found using the VQE algorithm. It is widely known that plane-wave methods struggle in describing local properties such as defects. Using the software Wannier90, it is possible to project the Kohn-Sham plane-waves based orbital onto a basis set of Wannier orbitals. Thus, we enable writing the Hamiltonian in a Wannier orbitals basis set and performing a VQE ground-state search. This optimized approach promises to provide accurate descriptions of both the pristine alloy and, in subsequent stages, hydrogen diffusion.