Ionic pseudopotentials are widely used in classical simulations of materials
to model the effective potential due to the nucleus and the core electrons.
Modeling fewer electrons explicitly results in a reduction in the number of
plane waves needed to accurately represent the states of a system. In this
work, we introduce a quantum algorithm that uses pseudopotentials to reduce the
cost of simulating periodic materials on a quantum computer. We use a
qubitization-based quantum phase estimation algorithm that employs a
first-quantization representation of the Hamiltonian in a plane-wave basis. We
address the challenge of incorporating the complexity of pseudopotentials into
quantum simulations by developing highly-optimized compilation strategies for
the qubitization of the Hamiltonian. This includes a linear combination of
unitaries decomposition that leverages the form of separable pseudopotentials.
Our strategies make use of quantum read-only memory subroutines as a more
efficient alternative to quantum arithmetic. We estimate the computational cost
of applying our algorithm to simulating lithium-excess cathode materials for
batteries, where more accurate simulations are needed to inform strategies for
gaining reversible access to the excess capacity they offer. We estimate the
number of qubits and Toffoli gates required to perform sufficiently accurate
simulations with our algorithm for three materials: lithium manganese oxide,
lithium nickel-manganese oxide, and lithium manganese oxyfluoride. Our
optimized compilation strategies result in a pseudopotential-based quantum
algorithm with a total runtime four orders of magnitude lower than the previous
state of the art for a fixed target accuracy