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For many-body methods such as MCSCF and CASSCF, in which the number ofone-electron orbitals are optimized and independent of basis set used, thereare no problems with using plane-wave basis sets. However, for methodscurrently used in quantum computing such as select configuration interaction(CI) and coupled cluster (CC) methods, it is necessary to have a virtual spacethat is able to capture a significant amount of electron-electron correlationin the system. The virtual orbitals in a pseudopotential plane-waveHartree--Fock calculation, because of Coulomb repulsion, are often scatteringstates that interact very weakly with the filled orbitals. As a result, verylittle correlation energy is captured from them. The use of virtual spacesderived from the one-electron operators have also been tried, and while somecorrelation is captured, the amount is quite low. To overcome theselimitations, we have been developing new classes of algorithms to definevirtual spaces by optimizing orbitals from small pairwise CI Hamiltonians,which we term as correlation optimized virtual orbitals with the abbreviationCOVOs. With these procedures we have been able to derive virtual spaces,containing only a few orbitals, that are able to capture a significant amountof correlation. Besides, using these derived basis sets for quantum computingcalculations targeting full CI (FCI) quality-results, they can also be used inother many-body approaches, including CC and M{\o}ller--Plesset perturbationtheories, and open up the door to many-body calculations for pseudopotentialplane-wave basis set methods. For the H$_2$ molecule, we were able to obtaingood agreement with FCI/cc-pVTZ results with just 4 virtual orbitals, for bothFCI and quantum simulations.

Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations