  The method of increments and frozen natural orbital (MI-FNO) framework is
introduced to help expedite the application of noisy, intermediate-scale
quantum~(NISQ) devices for quantum chemistry simulations. The MI-FNO framework
provides a systematic reduction of the occupied and virtual orbital spaces for
quantum chemistry simulations. The correlation energies of the resulting
increments from the MI-FNO reduction can then be solved by various algorithms,
including quantum algorithms such as the phase estimation algorithm and the
variational quantum eigensolver (VQE). The unitary coupled-cluster singles and
doubles VQE framework is used to obtain correlation energies for the case of
small molecules (i.e., BeH$_2$, CH$_4$, NH$_3$, H$_2$O, and HF) using the
cc-pVDZ basis set. The quantum resource requirements are estimated for a
constrained geometry complex (CGC) catalyst that is utilized in industrial
settings for the polymerization of $\alpha$-olefins. We show that the MI-FNO
approach provides a significant reduction in the qubit requirements relative to
the full system simulations. We propose that the MI-FNO framework can create
scalable examples of quantum chemistry problems that are appropriate for
assessing the progress of NISQ devices.

Quantum Physics