Enhancing initial state overlap through orbital optimization for faster molecular electronic ground-state energy estimation

TL;DR

This paper introduces an orbital optimization technique to improve the initial state overlap in quantum algorithms for molecular ground-state energy estimation, significantly reducing the required runtime for larger systems.

Contribution

It presents a practical orbital optimization method that enhances initial state overlap without prior ground state knowledge, demonstrated on iron-sulfur molecules.

Findings

Improved overlap by one to two orders of magnitude for tested molecules

Optimization reduces exponential decay of overlap with system size

Method outperforms localized molecular orbitals in initial state preparation

Abstract

The quantum phase estimation algorithm stands as the primary method for determining the ground state energy of a molecular electronic Hamiltonian on a quantum computer. In this context, the ability to initialize a classically tractable state that has a strong overlap with the desired ground state is critical as it directly affects the runtime of the algorithm. However, several numerical studies have shown that this overlap decays exponentially with system size. In this work, we demonstrate that this decay can be alleviated by optimizing the molecular orbital basis, for an initial state constructed from a single Slater determinant. We propose a practical method to achieve this optimization without knowledge of the true molecular ground state and test this method numerically. By comparing the resulting optimized orbitals to the natural orbitals, we find improved overlap. Specifically, for four iron-sulfur molecules, which are known to suffer from the mentioned decay, we show that our method yields one to two orders of magnitude improvement compared to localized molecular orbitals.