Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size

TL;DR

This paper introduces a quantum algorithm for simulating quantum chemistry that significantly reduces the complexity's dependence on basis size, enabling more efficient simulations especially for large basis sets.

Contribution

The authors develop a quantum simulation algorithm with sublinear scaling in basis size, outperforming previous methods for large N and small η in quantum chemistry simulations.

Findings

Achieves gate complexity $ ilde{O}(N^{1/3} ext{eta}^{8/3})$

Outperforms prior algorithms when $N o ext{large}$ and $ ext{eta}$ is small

Effective in first quantization using interaction picture techniques

Abstract

We present a quantum algorithm for simulating quantum chemistry with gate complexity $\tilde{O}(N^{1/3} \eta^{8/3})$ where $\eta$ is the number of electrons and $N$ is the number of plane wave orbitals. In comparison, the most efficient prior algorithms for simulating electronic structure using plane waves (which are at least as efficient as algorithms using any other basis) have complexity $\tilde{O}(N^{8/3} /\eta^{2/3})$. We achieve our scaling in first quantization by performing simulation in the rotating frame of the kinetic operator using interaction picture techniques. Our algorithm is far more efficient than all prior approaches when $N \gg \eta$, as is needed to suppress discretization error when representing molecules in the plane wave basis, or when simulating without the Born-Oppenheimer approximation.