Quantum techniques for eigenvalue problems

TL;DR

This paper introduces quantum algorithms for solving eigenvalue problems in quantum many-body systems, focusing on conceptual understanding of methods like adiabatic evolution, variational techniques, and phase detection, along with their advantages and challenges.

Contribution

It provides a focused overview of key quantum algorithms for eigenvalue problems, emphasizing their principles and potential benefits in quantum many-body systems.

Findings

Highlights advantages of quantum algorithms over classical methods.

Discusses remaining challenges in implementing these quantum techniques.

Provides conceptual clarity on various quantum eigenvalue algorithms.

Abstract

This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that cover the essentials of adiabatic evolution, variational methods, phase detection algorithms, and several other approaches. For each method, we discuss the potential advantages and remaining challenges.