Efficient state preparation for the quantum simulation of molecules in first quantization

TL;DR

This paper introduces an efficient method for preparing initial quantum states for molecular simulations, achieving logarithmic scaling in basis set size and enabling practical quantum simulation of larger molecules.

Contribution

It presents a novel approach to map Gaussian orbital basis states to plane wave basis states with logarithmic complexity, improving state preparation efficiency.

Findings

Achieves logarithmic scaling in basis set size for state preparation

Allows quantum simulation of larger molecules with fewer resources

Experimental results show significant reduction in non-Clifford gates

Abstract

The quantum simulation of real molecules and materials is one of the most highly anticipated applications of quantum computing. Algorithms for simulating electronic structure using a first-quantized plane wave representation are especially promising due to their asymptotic efficiency. However, previous proposals for preparing initial states for these simulation algorithms scale poorly with the size of the basis set. We address this shortcoming by showing how to efficiently map states defined in a Gaussian type orbital basis to a plane wave basis with a scaling that is logarithmic in the number of plane waves. Our key technical result is a proof that molecular orbitals constructed from Gaussian type basis functions can be compactly represented in a plane wave basis using matrix product states. While we expect that other approaches could achieve the same logarithmic scaling with respect to basis set size, our proposed state preparation technique is also highly efficient in practice. For example, in a series of numerical experiments on small molecules, we find that our approach allows us to prepare an approximation to the Hartree-Fock state using orders of magnitude fewer non-Clifford gates than a naive approach. By resolving the issue of state preparation, our work allows for the first quantum simulation of molecular systems whose end-to-end complexity is truly sublinear in the basis set size.