Transforming two-dimensional tensor networks into quantum circuits for supervised learning
There have been numerous quantum neural networks reported, but they struggle to match traditional neural networks in accuracy. Given the huge improvement of the neural network models’ accuracy by two-dimensional tensor network (TN) states in classical tensor network machine learning (TNML), it is pr...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/ad2fec |
| _version_ | 1797262280741617664 |
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| author | Zhihui Song Jinchen Xu Xin Zhou Xiaodong Ding Zheng Shan |
| author_facet | Zhihui Song Jinchen Xu Xin Zhou Xiaodong Ding Zheng Shan |
| author_sort | Zhihui Song |
| collection | DOAJ |
| description | There have been numerous quantum neural networks reported, but they struggle to match traditional neural networks in accuracy. Given the huge improvement of the neural network models’ accuracy by two-dimensional tensor network (TN) states in classical tensor network machine learning (TNML), it is promising to explore whether its application in quantum machine learning can extend the performance boundary of the models. Here, we transform two-dimensional TNs into quantum circuits for supervised learning. Specifically, we encode two-dimensional TNs into quantum circuits through rigorous mathematical proofs for constructing model ansätze, including string-bond states, entangled-plaquette states and isometric TN states. In addition, we propose adaptive data encoding methods and combine with TNs. We construct a tensor-network-inspired quantum circuit (TNQC) supervised learning framework for transferring TNML from classical to quantum, and build several novel two-dimensional TN-inspired quantum classifiers based on this framework. Finally, we propose a parallel quantum machine learning method for multi-class classification to construct 2D TNQC-based multi-class classifiers. Classical simulation results on the MNIST benchmark dataset show that our proposed models achieve the state-of-the-art accuracy performance, significantly outperforming other quantum classifiers on both binary and multi-class classification tasks, and beat simple convolutional classifiers on a fair track with identical inputs. The noise resilience of the models makes them successfully run and work in a real quantum computer. |
| first_indexed | 2024-04-24T23:54:36Z |
| format | Article |
| id | doaj.art-f999f6fd687b443095ca2b84225931de |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-04-24T23:54:36Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-f999f6fd687b443095ca2b84225931de2024-03-14T14:36:03ZengIOP PublishingMachine Learning: Science and Technology2632-21532024-01-015101504810.1088/2632-2153/ad2fecTransforming two-dimensional tensor networks into quantum circuits for supervised learningZhihui Song0https://orcid.org/0009-0006-6250-7896Jinchen Xu1Xin Zhou2Xiaodong Ding3https://orcid.org/0000-0001-9947-4035Zheng Shan4Information Engineering University , Zhengzhou 450001, People’s Republic of ChinaInformation Engineering University , Zhengzhou 450001, People’s Republic of China; Songshan Laboratory , Zhengzhou 450001, People’s Republic of ChinaInformation Engineering University , Zhengzhou 450001, People’s Republic of ChinaInformation Engineering University , Zhengzhou 450001, People’s Republic of ChinaInformation Engineering University , Zhengzhou 450001, People’s Republic of China; Songshan Laboratory , Zhengzhou 450001, People’s Republic of ChinaThere have been numerous quantum neural networks reported, but they struggle to match traditional neural networks in accuracy. Given the huge improvement of the neural network models’ accuracy by two-dimensional tensor network (TN) states in classical tensor network machine learning (TNML), it is promising to explore whether its application in quantum machine learning can extend the performance boundary of the models. Here, we transform two-dimensional TNs into quantum circuits for supervised learning. Specifically, we encode two-dimensional TNs into quantum circuits through rigorous mathematical proofs for constructing model ansätze, including string-bond states, entangled-plaquette states and isometric TN states. In addition, we propose adaptive data encoding methods and combine with TNs. We construct a tensor-network-inspired quantum circuit (TNQC) supervised learning framework for transferring TNML from classical to quantum, and build several novel two-dimensional TN-inspired quantum classifiers based on this framework. Finally, we propose a parallel quantum machine learning method for multi-class classification to construct 2D TNQC-based multi-class classifiers. Classical simulation results on the MNIST benchmark dataset show that our proposed models achieve the state-of-the-art accuracy performance, significantly outperforming other quantum classifiers on both binary and multi-class classification tasks, and beat simple convolutional classifiers on a fair track with identical inputs. The noise resilience of the models makes them successfully run and work in a real quantum computer.https://doi.org/10.1088/2632-2153/ad2fecquantum machine learningtwo-dimensional tensor networksvariational data encodingmachine learning interpretability |
| spellingShingle | Zhihui Song Jinchen Xu Xin Zhou Xiaodong Ding Zheng Shan Transforming two-dimensional tensor networks into quantum circuits for supervised learning Machine Learning: Science and Technology quantum machine learning two-dimensional tensor networks variational data encoding machine learning interpretability |
| title | Transforming two-dimensional tensor networks into quantum circuits for supervised learning |
| title_full | Transforming two-dimensional tensor networks into quantum circuits for supervised learning |
| title_fullStr | Transforming two-dimensional tensor networks into quantum circuits for supervised learning |
| title_full_unstemmed | Transforming two-dimensional tensor networks into quantum circuits for supervised learning |
| title_short | Transforming two-dimensional tensor networks into quantum circuits for supervised learning |
| title_sort | transforming two dimensional tensor networks into quantum circuits for supervised learning |
| topic | quantum machine learning two-dimensional tensor networks variational data encoding machine learning interpretability |
| url | https://doi.org/10.1088/2632-2153/ad2fec |
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