Efficient simulation of materials on fault-tolerant quantum computers using translational symmetries

Here we extend the infrastructure recently used in fault tolerant simulation of molecules to material systems defined over Bloch orbitals in second quantization. We demonstrate how to construct qubitized phase estimation oracles using various block encodings that take advantage of translational symmetry leading to a savings inversely proportional to the number of k-points sampled. We highlight this savings through a comparison to generic supercell simulations leveraging unmodified molecular algorithms for various simple systems and a Lithium Nickel Oxide battery cathode material. To identify potential quantum simulation advantage we compared quantum runtimes as a function of accuracy to flagship electronic structure simulations of the Lithium Nickel Oxide cathode material and other strongly correlated systems.