Unsupervised Classification of Quantum Data
We introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are of two types. Our protocol is universal and able to automatic...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-11-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.9.041029 |
| _version_ | 1818718432113197056 |
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| author | Gael Sentís Alex Monràs Ramon Muñoz-Tapia John Calsamiglia Emilio Bagan |
| author_facet | Gael Sentís Alex Monràs Ramon Muñoz-Tapia John Calsamiglia Emilio Bagan |
| author_sort | Gael Sentís |
| collection | DOAJ |
| description | We introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are of two types. Our protocol is universal and able to automatically sort the input under minimal assumptions, yet partially preserves information contained in the states. We quantify analytically its performance for an arbitrary size and dimension of the data. We contrast it with the performance of its classical counterpart, which clusters data that have been sampled from two unknown probability distributions. We find that the quantum protocol fully exploits the dimensionality of the quantum data to achieve a much higher performance, provided the data are at least three dimensional. For the sake of comparison, we discuss the optimal protocol when the classical and quantum states are known. |
| first_indexed | 2024-12-17T19:50:57Z |
| format | Article |
| id | doaj.art-2dd0f1f77043465c813abfa113b195a2 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-17T19:50:57Z |
| publishDate | 2019-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-2dd0f1f77043465c813abfa113b195a22022-12-21T21:34:44ZengAmerican Physical SocietyPhysical Review X2160-33082019-11-019404102910.1103/PhysRevX.9.041029Unsupervised Classification of Quantum DataGael SentísAlex MonràsRamon Muñoz-TapiaJohn CalsamigliaEmilio BaganWe introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are of two types. Our protocol is universal and able to automatically sort the input under minimal assumptions, yet partially preserves information contained in the states. We quantify analytically its performance for an arbitrary size and dimension of the data. We contrast it with the performance of its classical counterpart, which clusters data that have been sampled from two unknown probability distributions. We find that the quantum protocol fully exploits the dimensionality of the quantum data to achieve a much higher performance, provided the data are at least three dimensional. For the sake of comparison, we discuss the optimal protocol when the classical and quantum states are known.http://doi.org/10.1103/PhysRevX.9.041029 |
| spellingShingle | Gael Sentís Alex Monràs Ramon Muñoz-Tapia John Calsamiglia Emilio Bagan Unsupervised Classification of Quantum Data Physical Review X |
| title | Unsupervised Classification of Quantum Data |
| title_full | Unsupervised Classification of Quantum Data |
| title_fullStr | Unsupervised Classification of Quantum Data |
| title_full_unstemmed | Unsupervised Classification of Quantum Data |
| title_short | Unsupervised Classification of Quantum Data |
| title_sort | unsupervised classification of quantum data |
| url | http://doi.org/10.1103/PhysRevX.9.041029 |
| work_keys_str_mv | AT gaelsentis unsupervisedclassificationofquantumdata AT alexmonras unsupervisedclassificationofquantumdata AT ramonmunoztapia unsupervisedclassificationofquantumdata AT johncalsamiglia unsupervisedclassificationofquantumdata AT emiliobagan unsupervisedclassificationofquantumdata |