Emerging quantum computing algorithms for quantum chemistry

TL;DR

This review discusses recent advances in quantum algorithms for simulating molecular electronic structures, highlighting their theoretical foundations, implementation challenges, and potential for quantum chemistry applications.

Contribution

It provides a comprehensive overview of emerging quantum algorithms for electronic structure simulation, emphasizing their theoretical basis and recent progress.

Findings

Quantum algorithms show promise for molecular simulations.

Recent advances improve algorithm efficiency and accuracy.

Hardware limitations still pose challenges for practical implementation.

Abstract

Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed remarkable growth, notwithstanding the limitations of existing quantum hardware, especially as a tool for electronic structure computations in molecules. In this review, we provide a self-contained introduction to emerging algorithms for the simulation of Hamiltonian dynamics and eigenstates, with emphasis on their applications to the electronic structure in molecular systems. Theoretical foundations and implementation details of the method are discussed, and their strengths, limitations, and recent advances are presented.