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Generalization in Quantum Machine Learning from Few Training Data by Caro, Matthias C.; Huang, Hsin-Yuan; Cerezo, M.; Sharma, Kunal; Sornborger, Andrew; Cincio, Lukasz; Coles, Patrick J. is a scholarly article available to read on EtoBox.

What is Generalization in Quantum Machine Learning from Few Training Data about?

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number $N$ of training data points. We show that the generalization error of a quantum machine learning model with $T$ trainable gates scales at worst as $\sqrt{T/N}$. When only $K \ll T$ gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $\sqrt{K / N}$. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field

Author

Caro, Matthias C.; Huang, Hsin-Yuan; Cerezo, M.; Sharma, Kunal; Sornborger, Andrew; Cincio, Lukasz; Coles, Patrick J.

Published

2021

Language

EN