Warm-Starting the VQE with Approximate Complex Amplitude Encoding

• URL: http://arxiv.org/abs/2402.17378v1
• Date: Tue, 27 Feb 2024 10:15:25 GMT
• Title: Warm-Starting the VQE with Approximate Complex Amplitude Encoding
• Authors: Felix Truger, Johanna Barzen, Frank Leymann, Julian Obst
• Abstract summary: The Variational Quantum Eigensolver (VQE) is a quantum algorithm to determine the ground state of quantum-mechanical systems. We propose a warm-starting technique, that utilizes an approximation to generate beneficial initial parameter values for the VQE. Such warm-starts open the path to fruitful combinations of classical approximation algorithms and quantum algorithms.
• Score: 0.26217304977339473
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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