Dimensionality reduction of many-body problem using coupled-cluster sub-system flow equations: classical and quantum computing perspective

TL;DR

This paper presents a novel approach to reduce the complexity of many-body problems using coupled-cluster sub-system flow equations, applicable in both classical and quantum computing contexts, enabling more efficient simulations.

Contribution

It introduces a reduced-scaling framework employing SES-CC formalism and flow equations, enhancing the efficiency of many-body system modeling in classical and quantum computing.

Findings

Flow equations can be integrated into reduced-dimensionality eigenvalue problems.

Local flow formulations relate correlation effects to localized sub-systems.

The approach extends to time domain and quantum resource-efficient methods.

Abstract

We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub-systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be determined at the level of the CC Ansatz by the inclusion of selected classes of cluster amplitudes, which define the wave function "memory" of possible partitionings of the many-body system into constituent sub-systems. One of the possible ways of solving these coupled problems is through implementing procedures, where the information is passed between the sub-systems in a self-consistent manner. As a special case, we consider local flow formulations where the so-called local character of correlation effects can be closely related to properties of sub-system embedding sub-algebras employing localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing double exponential unitary CC Ansatz (DUCC), where reduced dimensionality of constituent sub-problems offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.