Structural risk minimization for quantum linear classifiers
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-01-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-01-13-893/pdf/ |
| _version_ | 1797953752111513600 |
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| author | Casper Gyurik Dyon Vreumingen, van Vedran Dunjko |
| author_facet | Casper Gyurik Dyon Vreumingen, van Vedran Dunjko |
| author_sort | Casper Gyurik |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T23:07:05Z |
| format | Article |
| id | doaj.art-b669c8bf722c47a4aeafbe5e668b642b |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-10T23:07:05Z |
| publishDate | 2023-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-b669c8bf722c47a4aeafbe5e668b642b2023-01-13T10:43:33ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-01-01789310.22331/q-2023-01-13-89310.22331/q-2023-01-13-893Structural risk minimization for quantum linear classifiersCasper GyurikDyon Vreumingen, vanVedran DunjkoQuantum 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.https://quantum-journal.org/papers/q-2023-01-13-893/pdf/ |
| spellingShingle | Casper Gyurik Dyon Vreumingen, van Vedran Dunjko Structural risk minimization for quantum linear classifiers Quantum |
| title | Structural risk minimization for quantum linear classifiers |
| title_full | Structural risk minimization for quantum linear classifiers |
| title_fullStr | Structural risk minimization for quantum linear classifiers |
| title_full_unstemmed | Structural risk minimization for quantum linear classifiers |
| title_short | Structural risk minimization for quantum linear classifiers |
| title_sort | structural risk minimization for quantum linear classifiers |
| url | https://quantum-journal.org/papers/q-2023-01-13-893/pdf/ |
| work_keys_str_mv | AT caspergyurik structuralriskminimizationforquantumlinearclassifiers AT dyonvreumingenvan structuralriskminimizationforquantumlinearclassifiers AT vedrandunjko structuralriskminimizationforquantumlinearclassifiers |