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

TL;DR

This work evaluates whether fault-tolerant quantum computers can meaningfully accelerate the discovery of homogeneous nitrogen-fixation catalysts by framing ground-state energy estimation as a benchmark problem. By comparing quantum phase estimation using double-factorized Hamiltonians against state-of-the-art classical methods (CC and DMRG) across three catalyst prototypes, the study quantifies logical and physical resource requirements, including up to ~10^12 Toffoli gates and ~10^6 physical qubits for high-utility cases. It introduces resource-reduction techniques like LPBLISS and analyzes their impact, demonstrating potential reductions in L1 norm and corresponding quantum costs. The findings suggest that with continued hardware and algorithmic advances, quantum computers could offer practical advantages for catalyst design, particularly in challenging nitrogen-fixation systems, while also outlining the economic and funding context for such computational approaches.

Abstract

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.

Figures (11)

• Figure 1: Molecules included for the Schrock catalyst, focused on the first step of the catalytic cycle, in which the base catalyst MoN$_2$ is reduced to MoN$_2^{-}$ by ferrocene Fe(Cp)$_2$.
• Figure 2: Molecules included for the Bridged Dimolybdenum Complex, focused on the initial protonation step in which a terminal nitrogen ligand of $1$-Lut$_{Re}$ is protonated to II-Lut$_{Prod}$ through transition state $1$-Lut$_{TS}$.
• Figure 3: Molecules included for the Molybdenum Pincer Complex, focused on the two steps of the catalytic cycle. During step (i), the reactant complex RC transforms into PC via TS$_{1/2}$, following which the released Cl$^-$ migrates to its ultimate position, forming $2$. In step (ii), the reduction of complex $2$ initiates the cleavage of the C--OPh bond in complex I, leading to the formation of PC$^-$ via TS$_{I/4a}$. PC$^-$ includes complex 4a and a released OPh$^-$.
• Figure 4: Example DMRG convergence plot, for Mo Pincer complex 2 using the smaller active space. Inset is a zoomed-in version of the main axes. Total wall time for these calculations on the Niagara computer cluster is about 4 hrs.
• Figure 5: Differences between the DMRG extrapolated energy and the CCSD/CCSD(T) energies for the nitrogen catalyst Hamiltonians, grouped according to reaction: [a] Schrock; [b] Bridged Dimolybdenum; [c] Mo Pincer reaction, step (i) smaller active space; [d] Mo Pincer reaction, step (i) larger active space; [e] Mo Pincer reaction, step (ii) smaller active space; and [f] Mo Pincer reaction, step (ii) larger active space. "Sm" and "Lg" refer to smaller and larger active spaces, respectively, and "NC" indicates the CCSD calculations that did not converge.