The power of quantum neural networks

It is unknown whether near-term quantum computers are advantageous for machine learning tasks. In this work we address this question by trying to understand how powerful and trainable quantum machine learning models are in relation to popular classical neural networks. We propose the effective dimension-a measure that captures these qualities-and prove that it can be used to assess any statistical model's ability to generalize on new data. Crucially, the effective dimension is a data-dependent measure that depends on the Fisher information, which allows us to gauge the ability of a model to train. We demonstrate numerically that a class of quantum neural networks is able to achieve a considerably better effective dimension than comparable feedforward networks and train faster, suggesting an advantage for quantum machine learning, which we verify on real quantum hardware.

Automated summary

This study investigates the advantage of near-term quantum computers for machine learning tasks by comparing the power and trainability of quantum machine learning models with classical neural networks. The effective dimension, a data-dependent measure based on Fisher information, is proposed to evaluate a model's ability to generalize on new data. Numerical demonstrations show that quantum neural networks outperform comparable feedforward networks in effective dimension and training speed, indicating an advantage for quantum machine learning validated on real quantum hardware.