Authors:
Felix Truger
;
Johanna Barzen
;
Frank Leymann
and
Julian Obst
Affiliation:
Institute of Architecture of Application Systems, University of Stuttgart, Universitätsstraße 38, Stuttgart, Germany
Keyword(s):
Variational Quantum Algorithm, Eigenvalues, Warm-Start, Classical Shadows.
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 qua
lity solutions earlier than the original VQE.
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