  The industrial manufacturing of chemicals consumes a significant amount of
energy and raw materials. In principle, the development of new catalysts could
greatly improve the efficiency of chemical production. However, the discovery
of viable catalysts can be exceedingly challenging because it is difficult to
know the efficacy of a candidate without experimentally synthesizing and
characterizing it. This study explores the feasibility of using fault-tolerant
quantum computers to accelerate the discovery of homogeneous catalysts for
nitrogen fixation, an industrially important chemical process. It introduces a
set of ground-state energy estimation problems representative of calculations
needed for the discovery of homogeneous catalysts and analyzes them on three
dimensions: economic utility, classical hardness, and quantum resource
requirements. For the highest utility problem considered, two steps of a
catalytic cycle for the generation of cyanate anion from dinitrogen, the
economic utility of running these computations is estimated to be $200,000, and
the required runtime for double-factorized phase estimation on a fault-tolerant
superconducting device is estimated under conservative assumptions to be
139,000 QPU-hours. The computational cost of an equivalent DMRG calculation is
estimated to be about 400,000 CPU-hours. These results suggest that, with
continued development, it will be feasible for fault-tolerant quantum computers
to accelerate the discovery of homogeneous catalysts.
