Coupled cluster downfolding techniques: a review of existing applications in classical and quantum computing for chemical systems

TL;DR

This review paper discusses recent advances in coupled cluster downfolding methods, which simplify quantum chemical calculations by creating effective Hamiltonians, and explores their applications in classical and quantum computing for chemical systems.

Contribution

It provides a comprehensive overview of various CC downfolding techniques, including extensions to time domain and quantum flows, highlighting their role in advancing quantum chemistry computations.

Findings

Enhanced understanding of CC downfolding methods

Extensions to time-dependent and quantum flow approaches

Potential for improved quantum chemical simulations on quantum computers

Abstract

In this manuscript, we provide an overview of the recent developments of the coupled cluster (CC) downfolding methods, where the ground-state problem of a quantum system is represented through effective/downfolded Hamiltonians defined using active spaces. All CC downfolding techniques discussed here are derived from a single-reference exponential ansatz for the ground-state problem. We discuss several extensions of the non-Hermitian and Hermitian downfolding approaches to the time domain and the so-called quantum flows. We emphasize the important role of downfolding formalisms in transitioning chemical applications from noisy quantum devices to scalable and error-corrected quantum computers.