Quantum distance approximation for persistence diagrams
Topological data analysis (TDA) methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially complex and high dimensional data sets. The space of per...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2025-01-01
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| Series: | Journal of Physics: Complexity |
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| Online Access: | https://doi.org/10.1088/2632-072X/ad9fca |
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| _version_ | 1832590573616234496 |
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| author | Bernardo Ameneyro Rebekah Herrman George Siopsis Vasileios Maroulas |
| author_facet | Bernardo Ameneyro Rebekah Herrman George Siopsis Vasileios Maroulas |
| author_sort | Bernardo Ameneyro |
| collection | DOAJ |
| description | Topological data analysis (TDA) methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially complex and high dimensional data sets. The space of persistence diagrams can be endowed with various metrics, which admit a statistical structure and allow to use these summaries for machine learning algorithms, e.g. the Wasserstein distance. However, computing the distance between two persistence diagrams involves finding an optimal way to match the points of the two diagrams and may not always be an easy task for classical computers. Recently, quantum algorithms have shown the potential to speedup the process of obtaining the persistence information displayed on persistence diagrams by estimating the spectra of persistent Dirac operators. So, in this work we explore the potential of quantum computers to estimate the distance between persistence diagrams as the next step in the design of a fully quantum framework for TDA. In particular we propose variational quantum algorithms for the Wasserstein distance as well as the $d^{c}_{p}$ distance. Our implementation is a weighted version of the quantum approximate optimization Algorithm that relies on control clauses to encode the constraints of the optimization problem. |
| format | Article |
| id | doaj-art-ed74699f73f14e8e937bac4a5c0e3d9c |
| institution | Kabale University |
| issn | 2632-072X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Journal of Physics: Complexity |
| spelling | doaj-art-ed74699f73f14e8e937bac4a5c0e3d9c2025-01-23T12:36:57ZengIOP PublishingJournal of Physics: Complexity2632-072X2025-01-016101500510.1088/2632-072X/ad9fcaQuantum distance approximation for persistence diagramsBernardo Ameneyro0https://orcid.org/0000-0002-6769-1219Rebekah Herrman1https://orcid.org/0000-0001-6944-4206George Siopsis2https://orcid.org/0000-0002-1466-2772Vasileios Maroulas3https://orcid.org/0000-0002-3412-6766Department of Mathematics, The University of Tennessee , Knoxville, TN 37996-1320, United States of AmericaDepartment of Industrial and Systems Engineering, The University of Tennessee , Knoxville, TN 37996, United States of AmericaDepartment of Physics and Astronomy, The University of Tennessee , Knoxville, TN 37996-1200, United States of AmericaDepartment of Mathematics, The University of Tennessee , Knoxville, TN 37996-1320, United States of AmericaTopological data analysis (TDA) methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially complex and high dimensional data sets. The space of persistence diagrams can be endowed with various metrics, which admit a statistical structure and allow to use these summaries for machine learning algorithms, e.g. the Wasserstein distance. However, computing the distance between two persistence diagrams involves finding an optimal way to match the points of the two diagrams and may not always be an easy task for classical computers. Recently, quantum algorithms have shown the potential to speedup the process of obtaining the persistence information displayed on persistence diagrams by estimating the spectra of persistent Dirac operators. So, in this work we explore the potential of quantum computers to estimate the distance between persistence diagrams as the next step in the design of a fully quantum framework for TDA. In particular we propose variational quantum algorithms for the Wasserstein distance as well as the $d^{c}_{p}$ distance. Our implementation is a weighted version of the quantum approximate optimization Algorithm that relies on control clauses to encode the constraints of the optimization problem.https://doi.org/10.1088/2632-072X/ad9fcatopological data analysisdistances of persistence diagramsquantum approximate optimization algorithms |
| spellingShingle | Bernardo Ameneyro Rebekah Herrman George Siopsis Vasileios Maroulas Quantum distance approximation for persistence diagrams Journal of Physics: Complexity topological data analysis distances of persistence diagrams quantum approximate optimization algorithms |
| title | Quantum distance approximation for persistence diagrams |
| title_full | Quantum distance approximation for persistence diagrams |
| title_fullStr | Quantum distance approximation for persistence diagrams |
| title_full_unstemmed | Quantum distance approximation for persistence diagrams |
| title_short | Quantum distance approximation for persistence diagrams |
| title_sort | quantum distance approximation for persistence diagrams |
| topic | topological data analysis distances of persistence diagrams quantum approximate optimization algorithms |
| url | https://doi.org/10.1088/2632-072X/ad9fca |
| work_keys_str_mv | AT bernardoameneyro quantumdistanceapproximationforpersistencediagrams AT rebekahherrman quantumdistanceapproximationforpersistencediagrams AT georgesiopsis quantumdistanceapproximationforpersistencediagrams AT vasileiosmaroulas quantumdistanceapproximationforpersistencediagrams |