Limitations of Hartree-Fock with quantum resources

TL;DR

This paper critically examines the limitations of using quantum resources for solving the Hartree-Fock problem, revealing fundamental challenges that hinder quantum advantage in this area.

Contribution

It provides a comprehensive analysis showing that the Hartree-Fock problem remains computationally challenging for quantum computers, limiting their potential benefits in quantum chemistry.

Findings

Hartree-Fock problem is computationally hard for quantum algorithms

Quantum resources do not significantly improve Hartree-Fock solutions

Energy landscapes for simple systems are fully characterized and complex

Abstract

The Hartree-Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the fundamental Hartree-Fock problem is a natural target. While quantum computers and quantum simulation offer many prospects for the future of modern chemistry, the Hartree-Fock problem is not a likely candidate. We highlight this fact from a number of perspectives including computational complexity, practical examples, and the full characterization of the energy landscapes for simple systems.