Quantum Simulations of Chemistry in First Quantization with any Basis Set

Quantum computation of the energy of molecules and materials is one of the most promising

applications of fault-tolerant quantum computers. Practical applications require development of

quantum algorithms with reduced resource requirements. Previous work has mainly focused on

quantum algorithms where the Hamiltonian is represented in second quantization with compact

basis sets while existing methods in first quantization are limited to a grid-based basis. In this work,

we present a new method to solve the generic ground-state chemistry problem in first quantization

using any basis set. We achieve asymptotic speedup in Toffoli count for molecular orbitals, and

orders of magnitude improvement using dual plane waves as compared to the second quantization

counterparts. In some instances, our approach provides similar or even lower resources compared to

previous first quantization plane wave algorithms that, unlike our approach, avoids the loading of

the classical data. This work opens up possibilities to reduce quantum resources even further using,

for example, factorization of a Hamiltonian and modern pseudopotentials.