Feasibility of accelerating homogeneous catalyst discovery with fault-tolerant quantum computers

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.