Warm-Starting the VQE with Approximate Complex Amplitude Encoding

Felix Truger, Johanna Barzen, Frank Leymann, Julian Obst

2025

Abstract

The Variational Quantum Eigensolver (VQE) is a Variational Quantum Algorithm (VQA) to determine the ground state of quantum-mechanical systems. As a VQA, it makes use of a classical computer to optimize parameter values for its quantum circuit. However, each iteration of the VQE requires a multitude of measurements, and the optimization is subject to obstructions, such as barren plateaus, local minima, and subsequently slow convergence. We propose a warm-starting technique, that utilizes an approximation to generate beneficial initial parameter values for the VQE aiming to mitigate these effects. The warm-start is based on Approximate Complex Amplitude Encoding, a VQA using fidelity estimations from classical shadows to encode complex amplitude vectors into quantum states. Such warm-starts open the path to fruitful combinations of classical approximation algorithms and quantum algorithms. In particular, the evaluation of our approach shows that the warm-started VQE reaches higher quality solutions earlier than the original VQE.

Paper Citation

in Harvard Style

Truger F., Barzen J., Leymann F. and Obst J. (2025). Warm-Starting the VQE with Approximate Complex Amplitude Encoding. In Proceedings of the 1st International Conference on Quantum Software - Volume 1: IQSOFT; ISBN 978-989-758-761-0, SciTePress, pages 15-26. DOI: 10.5220/0013513400004525

in Bibtex Style

@conference{iqsoft25,
author={Felix Truger and Johanna Barzen and Frank Leymann and Julian Obst},
title={Warm-Starting the VQE with Approximate Complex Amplitude Encoding},
booktitle={Proceedings of the 1st International Conference on Quantum Software - Volume 1: IQSOFT},
year={2025},
pages={15-26},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013513400004525},
isbn={978-989-758-761-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Quantum Software - Volume 1: IQSOFT
TI - Warm-Starting the VQE with Approximate Complex Amplitude Encoding
SN - 978-989-758-761-0
AU - Truger F.
AU - Barzen J.
AU - Leymann F.
AU - Obst J.
PY - 2025
SP - 15
EP - 26
DO - 10.5220/0013513400004525
PB - SciTePress