Eigenvector Continuation and Projection-Based Emulators

TL;DR

Eigenvector continuation is a subspace projection method for efficiently solving parametric eigenvalue problems, with applications in quantum systems and promising future developments.

Contribution

This paper provides a comprehensive overview of eigenvector continuation, including its development, theoretical foundations, and recent applications in quantum physics.

Findings

Effective for quantum system simulations

Demonstrates rapid convergence and accuracy

Applicable to a broad range of parametric eigenproblems

Abstract

Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of subspace-projection techniques called reduced-basis methods. In this colloquium article, we present the development, theory, and applications of eigenvector continuation and projection-based emulators. We introduce the basic concepts, discuss the underlying theory and convergence properties, and present recent applications for quantum systems and future prospects.