A coherent approach to quantum-classical optimization

TL;DR

This paper introduces a quantum-classical optimization protocol that uses Tensor Networks for pre-optimization, identifies coherence entropy as a key metric, and demonstrates improved performance in QAOA through extensive numerical validation.

Contribution

It presents a novel quantum-classical optimization method leveraging Tensor Networks and coherence entropy, enhancing initialization and efficiency in variational quantum algorithms.

Findings

Optimal initialization states are pure Gibbs states.

The proposed protocol significantly improves optimization effectiveness.

Numerical tests validate the approach's efficiency.

Abstract

Hybrid quantum-classical optimization techniques, which incorporate the pre-optimization of Variational Quantum Algorithms (VQAs) using Tensor Networks (TNs), have been shown to allow for the reduction of quantum computational resources. In the particular case of large optimization problems, commonly found in real-world use cases, this strategy is almost mandatory to reduce the otherwise unfathomable execution costs and improve the quality of the results. We identify the coherence entropy as a crucial metric in determining the suitability of quantum states as effective initialization candidates. Our findings are validated through extensive numerical tests for the Quantum Approximate Optimization Algorithm (QAOA), in which we find that the optimal initialization states are pure Gibbs states. Further, these results are explained with the inclusion of a simple and yet novel notion of expressivity adapted to classical optimization problems. Based on this finding, we propose a quantum-classical optimization protocol that significantly improves on previous approaches for such tasks, with specific focus on its effectiveness.