  Quantum computers are special purpose machines that are expected to be
particularly useful in simulating strongly correlated chemical systems. The
quantum computer excels at treating a moderate number of orbitals within an
active space in a fully quantum mechanical manner. We present a quantum phase
estimation calculation on F$_2$ in a (2,2) active space on Rigetti's Aspen-11
QPU. While this is a promising start, it also underlines the need for carefully
selecting the orbital spaces treated by the quantum computer. In this work, a
scheme for selecting such an active space automatically is described and
simulated results obtained using both the quantum phase estimation (QPE) and
variational quantum eigensolver (VQE) algorithms are presented and combined
with a subtractive method to enable accurate description of the environment.
The active occupied space is selected from orbitals localized on the chemically
relevant fragment of the molecule, while the corresponding virtual space is
chosen based on the magnitude of interactions with the occupied space
calculated from perturbation theory. This protocol is then applied to two
chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and
the photosenzitizer temoporfin. While the sizes of the active spaces currently
amenable to a quantum computational treatment are not enough to demonstrate
quantum advantage, the procedure outlined here is applicable to any active
space size, including those that are outside the reach of classical
computation.
