Warm-Starting the VQE with Approximate Complex Amplitude Encoding

TL;DR

This paper introduces a warm-starting method for the VQE using approximate complex amplitude encoding, which improves convergence speed and solution quality by leveraging classical shadow fidelity estimations.

Contribution

It presents a novel warm-start technique for VQE based on classical shadows, enhancing optimization efficiency and solution quality in quantum chemistry problems.

Findings

Warm-started VQE reaches higher quality solutions earlier.

The approach mitigates barren plateaus and local minima issues.

Classical shadow fidelity estimations effectively initialize quantum states.

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.