Structural risk minimization for quantum linear classifiers
This work addresses the limited understanding of generalization in quantum machine learning, offering incremental improvements for researchers in the field.
The paper tackles the problem of balancing training accuracy and generalization performance in quantum machine learning models by proving that two model parameters control both model complexity and correlation capture, leading to new structural risk minimization options.
Quantum machine learning (QML) models based on parameterized quantum circuits are often highlighted as candidates for quantum computing's near-term ``killer application''. However, the understanding of the empirical and generalization performance of these models is still in its infancy. In this paper we study how to balance between training accuracy and generalization performance (also called structural risk minimization) for two prominent QML models introduced by Havlíček et al. (Nature, 2019), and Schuld and Killoran (PRL, 2019). Firstly, using relationships to well understood classical models, we prove that two model parameters -- i.e., the dimension of the sum of the images and the Frobenius norm of the observables used by the model -- closely control the models' complexity and therefore its generalization performance. Secondly, using ideas inspired by process tomography, we prove that these model parameters also closely control the models' ability to capture correlations in sets of training examples. In summary, our results give rise to new options for structural risk minimization for QML models.