The topology of data hides in quantum thermal states
dc.contributor.author | Scali, S | |
dc.contributor.author | Umeano, C | |
dc.contributor.author | Kyriienko, O | |
dc.date.accessioned | 2024-07-17T14:39:35Z | |
dc.date.issued | 2024-07-11 | |
dc.date.updated | 2024-07-16T10:35:26Z | |
dc.description.abstract | We provide a quantum protocol to perform topological data analysis (TDA) via the distillation of quantum thermal states. Recent developments in quantum thermal state preparation algorithms reveal their characteristic scaling, defined by the properties of dissipative Lindbladians. This contrasts with protocols based on unitary evolution, which have a scaling depending on the properties of the combinatorial Laplacian. To leverage quantum thermal state preparation algorithms, we translate quantum TDA from a real-time to an imaginary-time picture, shifting the paradigm from a unitary approach to a dissipative one. Starting from an initial state overlapping with the ground state of the system, one can dissipate its energy via channels unique to the dataset, naturally distilling its information. Therefore, calculating Betti numbers translates into a purity estimation. Alternatively, this can be interpreted as the evaluation of the Rényi two-entropy, Uhlmann fidelity, or Hilbert–Schmidt distance relative to thermal states with the embedded topology of simplicial complexes. Our work opens the field of TDA toward a more physical interpretation of the topology of data. | en_GB |
dc.description.sponsorship | Innovate UK | en_GB |
dc.identifier.citation | Vol. 1, No. 3, article 036106 | en_GB |
dc.identifier.doi | https://doi.org/10.1063/5.0209201 | |
dc.identifier.grantnumber | 10030953 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/136746 | |
dc.identifier | ORCID: 0000-0002-8133-1551 (Scali, Stefano) | |
dc.identifier | ORCID: 0000-0002-6259-6570 (Kyriienko, Oleksandr) | |
dc.language.iso | en | en_GB |
dc.publisher | AIP Publishing | en_GB |
dc.rights | © 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). | en_GB |
dc.title | The topology of data hides in quantum thermal states | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2024-07-17T14:39:35Z | |
dc.description | This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record | en_GB |
dc.description | DATA AVAILABILITY: The data that support the findings of this study are available within the article. | en_GB |
dc.identifier.eissn | 2835-0103 | |
dc.identifier.journal | APL Quantum | en_GB |
dc.relation.ispartof | APL Quantum, 1(3) | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2024-06-18 | |
rioxxterms.version | AM | en_GB |
rioxxterms.licenseref.startdate | 2024-07-11 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2024-07-17T14:31:08Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2024-07-17T14:39:57Z | |
refterms.panel | B | en_GB |
refterms.dateFirstOnline | 2024-07-11 | |
exeter.rights-retention-statement | no |
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Except where otherwise noted, this item's licence is described as © 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).