Structural risk minimization for quantum linear classifiers

Quantum, vol. 7, pp. 893

Abstract

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. \cite{havlivcek:qsvm}, and Schuld and Killoran \cite{schuld:qsvm}. 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.

Authors 3

1. Casper Gyurik Aachen

   Leiden University

   Affiliation as printed

   LIACS, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, Netherlands

2. van Dyon Vreumingen Aachen

   Leiden University · University of Amsterdam · Institute of Physics · Centrum Wiskunde & Informatica · QuSoft

   Affiliation as printed

   Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands

   LIACS, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, Netherlands

   QuSoft, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, Netherlands

3. Vedran Dunjko Aachen

   Leiden University

   Affiliation as printed

   LIACS, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, Netherlands

   LION, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, Netherlands