Theoretical error performance analysis for variational quantum circuit based functional regression
Abstract The noisy intermediate-scale quantum devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require furth...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-01-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-022-00672-7 |
| _version_ | 1797952392489074688 |
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| author | Jun Qi Chao-Han Huck Yang Pin-Yu Chen Min-Hsiu Hsieh |
| author_facet | Jun Qi Chao-Han Huck Yang Pin-Yu Chen Min-Hsiu Hsieh |
| author_sort | Jun Qi |
| collection | DOAJ |
| description | Abstract The noisy intermediate-scale quantum devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require further investigation, particularly when the dimensionality of classical inputs is concerned. In this work, we first put forth an end-to-end QNN, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression. Then, we aim at the error performance analysis for the TTN-VQC in terms of representation and generalization powers. We also characterize the optimization properties of TTN-VQC by leveraging the Polyak-Lojasiewicz condition. Moreover, we conduct the experiments of functional regression on a handwritten digit classification dataset to justify our theoretical analysis. |
| first_indexed | 2024-04-10T22:45:37Z |
| format | Article |
| id | doaj.art-0aa8e36fafb14264a3b94148a182d514 |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-04-10T22:45:37Z |
| publishDate | 2023-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-0aa8e36fafb14264a3b94148a182d5142023-01-15T12:17:39ZengNature Portfolionpj Quantum Information2056-63872023-01-019111010.1038/s41534-022-00672-7Theoretical error performance analysis for variational quantum circuit based functional regressionJun Qi0Chao-Han Huck Yang1Pin-Yu Chen2Min-Hsiu Hsieh3Department of Electronic Engineering, School of Information Science and Engineering, Fudan UniversityElectrical and Computer Engineering, Georgia Institute of TechnologyIBM ResearchHon Hai Quantum Computing Research CenterAbstract The noisy intermediate-scale quantum devices enable the implementation of the variational quantum circuit (VQC) for quantum neural networks (QNN). Although the VQC-based QNN has succeeded in many machine learning tasks, the representation and generalization powers of VQC still require further investigation, particularly when the dimensionality of classical inputs is concerned. In this work, we first put forth an end-to-end QNN, TTN-VQC, which consists of a quantum tensor network based on a tensor-train network (TTN) for dimensionality reduction and a VQC for functional regression. Then, we aim at the error performance analysis for the TTN-VQC in terms of representation and generalization powers. We also characterize the optimization properties of TTN-VQC by leveraging the Polyak-Lojasiewicz condition. Moreover, we conduct the experiments of functional regression on a handwritten digit classification dataset to justify our theoretical analysis.https://doi.org/10.1038/s41534-022-00672-7 |
| spellingShingle | Jun Qi Chao-Han Huck Yang Pin-Yu Chen Min-Hsiu Hsieh Theoretical error performance analysis for variational quantum circuit based functional regression npj Quantum Information |
| title | Theoretical error performance analysis for variational quantum circuit based functional regression |
| title_full | Theoretical error performance analysis for variational quantum circuit based functional regression |
| title_fullStr | Theoretical error performance analysis for variational quantum circuit based functional regression |
| title_full_unstemmed | Theoretical error performance analysis for variational quantum circuit based functional regression |
| title_short | Theoretical error performance analysis for variational quantum circuit based functional regression |
| title_sort | theoretical error performance analysis for variational quantum circuit based functional regression |
| url | https://doi.org/10.1038/s41534-022-00672-7 |
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