  The electron pair approximation offers a resource efficient variational
quantum eigensolver (VQE) approach for quantum chemistry simulations on quantum
computers. With the number of entangling gates scaling quadratically with
system size and a constant energy measurement overhead, the orbital optimized
unitary pair coupled cluster double (oo-upCCD) ansatz strikes a balance between
accuracy and efficiency on today's quantum computers. However, the electron
pair approximation makes the method incapable of producing quantitatively
accurate energy predictions. In order to improve the accuracy without
increasing the circuit depth, we explore the idea of reduced density matrix
(RDM) based second order perturbation theory (PT2) as an energetic correction
to electron pair approximation. The new approach takes into account of the
broken-pair energy contribution that is missing in pair-correlated electron
simulations, while maintaining the computational advantages of oo-upCCD ansatz.
In dissociations of N$_2$, Li$_2$O, and chemical reactions such as the
unimolecular decomposition of CH$_2$OH$^+$ and the \snTwo reaction of CH$_3$I
$+$ Br$^-$, the method significantly improves the accuracy of energy
prediction. On two generations of the IonQ's trapped ion quantum computers,
Aria and Forte, we find that unlike the VQE energy, the PT2 energy correction
is highly noise-resilient. By applying a simple error mitigation approach based
on post-selection solely on the VQE energies, the predicted VQE-PT2 energy
differences between reactants, transition state, and products are in excellent
agreement with noise-free simulators.
