Regressions on quantum neural networks at maximal expressivity
Abstract Considering a universal deep neural network organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads we analyze its expressivity. This ability to approximate continuous functions in regression tasks is quantified making use of a partial Fourier decompositi...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-12-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-81436-5 |
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| author | Iván Panadero Yue Ban Hilario Espinós Ricardo Puebla Jorge Casanova Erik Torrontegui |
| author_facet | Iván Panadero Yue Ban Hilario Espinós Ricardo Puebla Jorge Casanova Erik Torrontegui |
| author_sort | Iván Panadero |
| collection | DOAJ |
| description | Abstract Considering a universal deep neural network organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads we analyze its expressivity. This ability to approximate continuous functions in regression tasks is quantified making use of a partial Fourier decomposition of the generated output and systematically benchmarked with the aid of a teacher-student scheme. While the maximal expressive power increases with the depth of the network and the number of qubits, it is fundamentally bounded by the data encoding mechanism. However, we show that the measurement of the network generated output drastically modifies the attainability of this bound. Global-entangling measurements on the network can saturate the maximal expressive bound leading to an enhancement of the approximation capabilities of the network compared to local readouts of the individual qubits in non-entangling networks. We attribute this enhancement to a larger survival set of Fourier harmonics when decomposing the output signal. |
| format | Article |
| id | doaj-art-95a4d90f93c6401d9a6c0d839801953a |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-95a4d90f93c6401d9a6c0d839801953a2025-01-05T12:24:53ZengNature PortfolioScientific Reports2045-23222024-12-0114111610.1038/s41598-024-81436-5Regressions on quantum neural networks at maximal expressivityIván Panadero0Yue Ban1Hilario Espinós2Ricardo Puebla3Jorge Casanova4Erik Torrontegui5Departamento de Física, Universidad Carlos III de MadridDepartamento de Física, Universidad Carlos III de MadridDepartamento de Física, Universidad Carlos III de MadridDepartamento de Física, Universidad Carlos III de MadridDepartment of Physical Chemistry, University of the Basque Country UPV/EHUDepartamento de Física, Universidad Carlos III de MadridAbstract Considering a universal deep neural network organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads we analyze its expressivity. This ability to approximate continuous functions in regression tasks is quantified making use of a partial Fourier decomposition of the generated output and systematically benchmarked with the aid of a teacher-student scheme. While the maximal expressive power increases with the depth of the network and the number of qubits, it is fundamentally bounded by the data encoding mechanism. However, we show that the measurement of the network generated output drastically modifies the attainability of this bound. Global-entangling measurements on the network can saturate the maximal expressive bound leading to an enhancement of the approximation capabilities of the network compared to local readouts of the individual qubits in non-entangling networks. We attribute this enhancement to a larger survival set of Fourier harmonics when decomposing the output signal.https://doi.org/10.1038/s41598-024-81436-5Quantum neural networksQuantum machine learning |
| spellingShingle | Iván Panadero Yue Ban Hilario Espinós Ricardo Puebla Jorge Casanova Erik Torrontegui Regressions on quantum neural networks at maximal expressivity Scientific Reports Quantum neural networks Quantum machine learning |
| title | Regressions on quantum neural networks at maximal expressivity |
| title_full | Regressions on quantum neural networks at maximal expressivity |
| title_fullStr | Regressions on quantum neural networks at maximal expressivity |
| title_full_unstemmed | Regressions on quantum neural networks at maximal expressivity |
| title_short | Regressions on quantum neural networks at maximal expressivity |
| title_sort | regressions on quantum neural networks at maximal expressivity |
| topic | Quantum neural networks Quantum machine learning |
| url | https://doi.org/10.1038/s41598-024-81436-5 |
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