  The quantum computation of electronic energies can break the curse of
dimensionality that plagues many-particle quantum mechanics. It is for this
reason that a universal quantum computer has the potential to fundamentally
change computational chemistry and materials science, areas in which strong
electron correlations present severe hurdles for traditional electronic
structure methods. Here, we present a state-of-the-art analysis of accurate
energy measurements on a quantum computer for computational catalysis, using
improved quantum algorithms with more than an order of magnitude improvement
over the best previous algorithms. As a prototypical example of local catalytic
chemical reactivity we consider the case of a ruthenium catalyst that can bind,
activate, and transform carbon dioxide to the high-value chemical methanol. We
aim at accurate resource estimates for the quantum computing steps required for
assessing the electronic energy of key intermediates and transition states of
its catalytic cycle. In particular, we present new quantum algorithms for
double-factorized representations of the four-index integrals that can
significantly reduce the computational cost over previous algorithms, and we
discuss the challenges of increasing active space sizes to accurately deal with
dynamical correlations. We address the requirements for future quantum hardware
in order to make a universal quantum computer a successful and reliable tool
for quantum computing enhanced computational materials science and chemistry,
and identify open questions for further research.
