The power of quantum neural networks

TL;DR

This paper investigates the expressibility and trainability of quantum neural networks using information geometry, demonstrating their potential advantages over classical neural networks in effective dimension and training speed, verified on real hardware.

Contribution

It introduces a new measure of expressibility for quantum models, connects Fisher information to trainability issues, and shows quantum neural networks can outperform classical ones in effective dimension and training speed.

Findings

Quantum neural networks have higher effective dimension than classical ones.

Certain quantum models are more resilient to barren plateaus, enabling faster training.

Experimental validation on real quantum hardware confirms theoretical advantages.

Abstract

Fault-tolerant quantum computers offer the promise of dramatically improving machine learning through speed-ups in computation or improved model scalability. In the near-term, however, the benefits of quantum machine learning are not so clear. Understanding expressibility and trainability of quantum models-and quantum neural networks in particular-requires further investigation. In this work, we use tools from information geometry to define a notion of expressibility for quantum and classical models. The effective dimension, which depends on the Fisher information, is used to prove a novel generalisation bound and establish a robust measure of expressibility. We show that quantum neural networks are able to achieve a significantly better effective dimension than comparable classical neural networks. To then assess the trainability of quantum models, we connect the Fisher information spectrum to barren plateaus, the problem of vanishing gradients. Importantly, certain quantum neural networks can show resilience to this phenomenon and train faster than classical models due to their favourable optimisation landscapes, captured by a more evenly spread Fisher information spectrum. Our work is the first to demonstrate that well-designed quantum neural networks offer an advantage over classical neural networks through a higher effective dimension and faster training ability, which we verify on real quantum hardware.