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

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.