  We provide an integration of the universal, perturbative explicitly
correlated [2]$_\text{R12}$-correction in the context of the Variational
Quantum Eigensolver (VQE). This approach is able to increase the accuracy of
the underlying reference method significantly while requiring no additional
quantum 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 are
then combined with a set of molecular integrals. This computation comes at a
cost that scales as the sixth power of the number of electrons. We explore the
performance of the VQE+[2]$_\text{R12}$ approach using both conventional
Gaussian basis sets and our recently proposed directly determined pair-natural
orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital
and PNOs are investigated as a potential set of complementary basis functions
in the computation of [2]$_\text{R12}$. In particular the combination of
MRA-PNOs with [2]$_\text{R12}$ has turned out to be very promising --
persistently throughout our data, this allowed very accurate simulations at a
quantum cost of a minimal basis set. Additionally, we found that the deployment
of PNOs as complementary basis can greatly reduce the number of complementary
basis functions that enter the computation of the correction at a cubic
complexity.
