Occupation Numbers as Reduced Variables for Variational Quantum Computing

Kimika Teorikoa Seminar

Occupation numbers (ONs) are the fundamental variational quantities of natural orbital functional (NOF) theory together with the natural orbitals, providing a reduced description of the electronic structure problem. Here, we investigate ONs as reduced variables for variational quantum computing. Two complementary formulations are considered. In ON variational quantum eigensolver, ONs are extracted directly from a many-electron state and used to evaluate the energy through a NOF. In occupation-space variational quantum optimization, occupation states replace the many-electron wavefunction as the quantum variational objects, with their measurement probabilities directly providing the ONs. We analyze the reduction in quantum measurement and representation requirements associated with these formulations and compare them for the symmetric dissociation of cubic H8. The results establish ONs as a direct interface between quantum computation and NOF theory, enabling variational quantum algorithms to operate on the reduced variables required for the electronic energy.