Journal Article

Theoretical guarantees for permutation-equivariant quantum neural networks

Nguyen, Quynh T., Schatzki, Louis, Cerezo, M., Larocca, Martín, Sauvage, Frédéric

2024

Overview

Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group S n ), and show how to build S n -equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML.

• Publisher: Nature Publishing Group UK,Nature Publishing Group,Nature Partner Journals,Nature Portfolio
• Subject: 639/705 / 639/766/483/481 / Classical and Quantum Gravitation / CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS / Learning algorithms / Machine learning / mathematics and computing / Neural networks / Physics / Physics and Astronomy / Quantum Computing / Quantum Field Theories / quantum information / Quantum Information Technology / Quantum Physics / Relativity Theory / Spintronics / String Theory