Theoretical guarantees for permutation-equivariant quantum neural networks
Abstract Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training lands...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-01-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-024-00804-1 |
| _version_ | 1797276394766467072 |
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| author | Louis Schatzki Martín Larocca Quynh T. Nguyen Frédéric Sauvage M. Cerezo |
| author_facet | Louis Schatzki Martín Larocca Quynh T. Nguyen Frédéric Sauvage M. Cerezo |
| author_sort | Louis Schatzki |
| collection | DOAJ |
| description | Abstract Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group S n ), and show how to build S n -equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML. |
| first_indexed | 2024-03-07T15:27:41Z |
| format | Article |
| id | doaj.art-544fa5184c2146dd91386ed3571ce267 |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-03-07T15:27:41Z |
| publishDate | 2024-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-544fa5184c2146dd91386ed3571ce2672024-03-05T16:37:34ZengNature Portfolionpj Quantum Information2056-63872024-01-0110111410.1038/s41534-024-00804-1Theoretical guarantees for permutation-equivariant quantum neural networksLouis Schatzki0Martín Larocca1Quynh T. Nguyen2Frédéric Sauvage3M. Cerezo4Information Sciences, Los Alamos National LaboratoryTheoretical Division, Los Alamos National LaboratoryTheoretical Division, Los Alamos National LaboratoryTheoretical Division, Los Alamos National LaboratoryInformation Sciences, Los Alamos National LaboratoryAbstract Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group S n ), and show how to build S n -equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML.https://doi.org/10.1038/s41534-024-00804-1 |
| spellingShingle | Louis Schatzki Martín Larocca Quynh T. Nguyen Frédéric Sauvage M. Cerezo Theoretical guarantees for permutation-equivariant quantum neural networks npj Quantum Information |
| title | Theoretical guarantees for permutation-equivariant quantum neural networks |
| title_full | Theoretical guarantees for permutation-equivariant quantum neural networks |
| title_fullStr | Theoretical guarantees for permutation-equivariant quantum neural networks |
| title_full_unstemmed | Theoretical guarantees for permutation-equivariant quantum neural networks |
| title_short | Theoretical guarantees for permutation-equivariant quantum neural networks |
| title_sort | theoretical guarantees for permutation equivariant quantum neural networks |
| url | https://doi.org/10.1038/s41534-024-00804-1 |
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