  Understanding the physics of strongly correlated materials is one of the
grand challenge problems for physics today. A large class of scientifically
interesting materials, from high-$T_c$ superconductors to spin liquids, involve
medium to strong correlations, and building a holistic understanding of these
materials is critical. Doing so is hindered by the competition between the
kinetic energy and Coulomb repulsion, which renders both analytic and numerical
methods unsatisfactory for describing interacting materials. Fault-tolerant
quantum computers have been proposed as a path forward to overcome these
difficulties, but this potential capability has not yet been fully assessed.
Here, using the multi-orbital Fermi-Hubbard model as a representative model and
a source of scalable problem specifications, we estimate the resource costs
needed to use fault-tolerant quantum computers for obtaining experimentally
relevant quantities such as correlation function estimation. We find that
advances in quantum algorithms and hardware will be needed in order to reduce
quantum resources and feasibly address utility-scale problem instances.
