Quantum chemistry, classical heuristics, and quantum advantage

TL;DR

This paper explores the intersection of quantum chemistry and quantum computing, analyzing classical heuristics, conjectured complexities, and potential quantum advantages to guide future research in the field.

Contribution

It provides a comprehensive overview of quantum chemistry problems, classical heuristics, and conjectured complexities, proposing avenues for quantum advantage and fostering interdisciplinary understanding.

Findings

Classical heuristics are effective in quantum chemistry problems.

A conjectured classical complexity for quantum chemistry problems is proposed.

Opportunities for quantum advantage are identified and classified.

Abstract

We describe the problems of quantum chemistry, the intuition behind classical heuristic methods used to solve them, a conjectured form of the classical complexity of quantum chemistry problems, and the subsequent opportunities for quantum advantage. This article is written for both quantum chemists and quantum information theorists. In particular, we attempt to summarize the domain of quantum chemistry problems as well as the chemical intuition that is applied to solve them within concrete statements (such as a classical heuristic cost conjecture and a classification of different avenues for quantum advantage) in the hope that this may stimulate future analysis.