Tensor network compressed sensing with unsupervised machine learning
We propose the tensor-network compressed sensing (TNCS) by incorporating the ideas of compressed sensing, tensor network (TN), and machine learning. The primary idea is to compress and communicate the real-life information through the generative TN state and by making projective measurements in a de...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-08-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.033293 |
| _version_ | 1797211337231695872 |
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| author | Shi-Ju Ran Zheng-Zhi Sun Shao-Ming Fei Gang Su Maciej Lewenstein |
| author_facet | Shi-Ju Ran Zheng-Zhi Sun Shao-Ming Fei Gang Su Maciej Lewenstein |
| author_sort | Shi-Ju Ran |
| collection | DOAJ |
| description | We propose the tensor-network compressed sensing (TNCS) by incorporating the ideas of compressed sensing, tensor network (TN), and machine learning. The primary idea is to compress and communicate the real-life information through the generative TN state and by making projective measurements in a designed way. First, the state |Ψ〉 is obtained by the unsupervised learning of TN, and then the data to be communicated are encoded in the separable state with the minimal distance to the projected state |Φ〉, where |Φ〉 can be acquired by partially projecting |Ψ〉. A protocol analogous to the compressed sensing assisted by neural-network machine learning is thus suggested, where the projections are designed to rapidly minimize the uncertainty of information in |Φ〉. To characterize the efficiency of TNCS, we propose a quantity named as q sparsity to describe the sparsity of quantum states, which is analogous to the sparsity of the signals required in the standard compressed sensing. The need of the q sparsity in TNCS is essentially due to the fact that the TN states obey the area law of entanglement entropy. The tests on the real-life data (handwritten digits and fashion images) show that the TNCS has competitive efficiency and accuracy. |
| first_indexed | 2024-04-24T10:24:53Z |
| format | Article |
| id | doaj.art-6f889bbe03994e05b1334ffaf295106a |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:24:53Z |
| publishDate | 2020-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-6f889bbe03994e05b1334ffaf295106a2024-04-12T16:59:20ZengAmerican Physical SocietyPhysical Review Research2643-15642020-08-012303329310.1103/PhysRevResearch.2.033293Tensor network compressed sensing with unsupervised machine learningShi-Ju RanZheng-Zhi SunShao-Ming FeiGang SuMaciej LewensteinWe propose the tensor-network compressed sensing (TNCS) by incorporating the ideas of compressed sensing, tensor network (TN), and machine learning. The primary idea is to compress and communicate the real-life information through the generative TN state and by making projective measurements in a designed way. First, the state |Ψ〉 is obtained by the unsupervised learning of TN, and then the data to be communicated are encoded in the separable state with the minimal distance to the projected state |Φ〉, where |Φ〉 can be acquired by partially projecting |Ψ〉. A protocol analogous to the compressed sensing assisted by neural-network machine learning is thus suggested, where the projections are designed to rapidly minimize the uncertainty of information in |Φ〉. To characterize the efficiency of TNCS, we propose a quantity named as q sparsity to describe the sparsity of quantum states, which is analogous to the sparsity of the signals required in the standard compressed sensing. The need of the q sparsity in TNCS is essentially due to the fact that the TN states obey the area law of entanglement entropy. The tests on the real-life data (handwritten digits and fashion images) show that the TNCS has competitive efficiency and accuracy.http://doi.org/10.1103/PhysRevResearch.2.033293 |
| spellingShingle | Shi-Ju Ran Zheng-Zhi Sun Shao-Ming Fei Gang Su Maciej Lewenstein Tensor network compressed sensing with unsupervised machine learning Physical Review Research |
| title | Tensor network compressed sensing with unsupervised machine learning |
| title_full | Tensor network compressed sensing with unsupervised machine learning |
| title_fullStr | Tensor network compressed sensing with unsupervised machine learning |
| title_full_unstemmed | Tensor network compressed sensing with unsupervised machine learning |
| title_short | Tensor network compressed sensing with unsupervised machine learning |
| title_sort | tensor network compressed sensing with unsupervised machine learning |
| url | http://doi.org/10.1103/PhysRevResearch.2.033293 |
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