Coupled Cluster Downfolding Theory: towards efficient many-body algorithms for dimensionality reduction of composite quantum systems

TL;DR

This paper explores advanced coupled cluster downfolding methods to create effective Hamiltonians for quantum many-body systems, aiming to improve dimensionality reduction and facilitate quantum computing applications.

Contribution

It extends non-Hermitian and Hermitian CC downfolding techniques to composite systems, enabling more efficient quantum simulations and local approaches.

Findings

Developed non-Hermitian and Hermitian downfolding formulations for composite systems.

Proposed algorithms for extracting inter-electron interactions in active spaces.

Discussed potential applications in quantum computing and local CC methods.

Abstract

The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.