Walking through Hilbert Space with Quantum Computers

TL;DR

This review discusses recent quantum algorithms for complex sampling in computational chemistry, highlighting their theoretical frameworks, potential advantages, and challenges in leveraging quantum computers for chemical simulations.

Contribution

It provides a comprehensive overview of quantum algorithms for sampling tasks in chemistry, comparing classical and quantum methods, and discussing their potential for quantum advantage.

Findings

Quantum algorithms show promise for chemical simulations.

Challenges remain in achieving quantum computational advantages.

Various sampling techniques are adapted for quantum computing.

Abstract

Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex sampling tasks in the key areas of computational chemistry: ground state, thermal state properties, and quantum dynamics calculations. We review a broad range of quantum algorithms, from hybrid quantum-classical to fully quantum, focusing on the traditional Monte Carlo family, including Markov chain Monte Carlo, variational Monte Carlo, projector Monte Carlo, path integral Monte Carlo, etc. We also cover other relevant techniques involving complex sampling tasks, such as quantum-selected configuration interaction, minimally entangled typical thermal states, entanglement forging, and Monte Carlo-flavored Lindbladian dynamics. We provide a comprehensive overview of these algorithms' classical and quantum counterparts, detailing their theoretical frameworks and discussing the potentials and challenges in achieving quantum computational advantages.