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We provide an integration of the universal, perturbative explicitlycorrelated [2]$_\text{R12}$-correction in the context of the VariationalQuantum Eigensolver (VQE). This approach is able to increase the accuracy ofthe underlying reference method significantly while requiring no additionalquantum resources. Our proposed approach only requires knowledge of the one-and two-particle reduced density matrices (RDMs) of the reference wavefunction;these can be measured after having reached convergence in VQE. The RDMs arethen combined with a set of molecular integrals. This computation comes at acost that scales as the sixth power of the number of electrons. We explore theperformance of the VQE+[2]$_\text{R12}$ approach using both conventionalGaussian basis sets and our recently proposed directly determined pair-naturalorbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbitaland PNOs are investigated as a potential set of complementary basis functionsin the computation of [2]$_\text{R12}$. In particular the combination ofMRA-PNOs with [2]$_\text{R12}$ has turned out to be very promising --persistently throughout our data, this allowed very accurate simulations at aquantum cost of a minimal basis set. Additionally, we found that the deploymentof PNOs as complementary basis can greatly reduce the number of complementarybasis functions that enter the computation of the correction at a cubiccomplexity.

Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative [2]-R12-Correction