A Practical Introduction to VQE: Methods, Challenges, and Applications in Physics and Chemistry
Abstract
The Variational Quantum Eigensolver (VQE) has become a central hybrid quantum-classical method for addressing electronic structure and materials science problems on near-term quantum hardware. As researchers across physics, chemistry, and quantum information engage with VQE, they encounter a wide range of algorithmic choices, including problem encoding, ansatz construction, classical optimization, and measurement strategies to choose from. This article provides a structured overview of these components and discusses practical factors that influence VQE performance in real settings, such as noise characteristics, available error-mitigation techniques, and hardware-dependent circuit considerations. Drawing partly on our early experiences, we highlight aspects that may be especially relevant for newcomers and outline common challenges observed in practical workflows. Our aim is to offer an accessible entry point for researchers approaching VQE-based quantum simulation and to support informed decision-making as the method and underlying hardware continue to evolve, which we support by discussion of examples from physics and quantum chemistry.
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BibTeX
@misc{ehrlich2026practical,
title = {{A Practical Introduction to VQE: Methods, Challenges, and Applications in Physics and Chemistry}},
author = {Jannis Ehrlich and Felix Rupprecht and Konstantin Lamp and Elias Walter and Alejandro D. Somoza and Manuel Enns and Christian Elsässer and Birger Horstmann and Daniel F. Urban},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06448},
eprint = {2610.06448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06448},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Practical Introduction to VQE: Methods, Challenges, and Applications in Physics and Chemistry
AU - Jannis Ehrlich
AU - Felix Rupprecht
AU - Konstantin Lamp
AU - Elias Walter
AU - Alejandro D. Somoza
AU - Manuel Enns
AU - Christian Elsässer
AU - Birger Horstmann
AU - Daniel F. Urban
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.06448
UR - https://arxiv.org/abs/2610.06448
AB - The Variational Quantum Eigensolver (VQE) has become a central hybrid quantum-classical method for addressing electronic structure and materials science problems on near-term quantum hardware. As researchers across physics, chemistry, and quantum information engage with VQE, they encounter a wide range of algorithmic choices, including problem encoding, ansatz construction, classical optimization, and measurement strategies to choose from. This article provides a structured overview of these components and discusses practical factors that influence VQE performance in real settings, such as noise characteristics, available error-mitigation techniques, and hardware-dependent circuit considerations. Drawing partly on our early experiences, we highlight aspects that may be especially relevant for newcomers and outline common challenges observed in practical workflows. Our aim is to offer an accessible entry point for researchers approaching VQE-based quantum simulation and to support informed decision-making as the method and underlying hardware continue to evolve, which we support by discussion of examples from physics and quantum chemistry.
ER -