Fault tolerant simulation of materials in 2nd quantization

An accurate assessment of how quantum computers can be used for chemical or materials simulation, especially their computational advantages, provides important context on how to deploy these future devices. To make this assessment we estimate the quantum resources required to sample the ground state of electronic structure Hamiltonians. This involves comparing various block encoding strategies, improving the block encoding constructions through symmetry-adapting, and ultimately compiling into the surface code to estimate physical qubit requirements and runtimes. To define a quantum simulation advantage we compare quantum runtime estimates to flagship classical simulations for a variety of challenging chemical and materials simulation problems.