Learning entanglement breakdown as a phase transition by confusion
Quantum technologies require methods for preparing and manipulating entangled multiparticle states. However, the problem of determining whether a given quantum state is entangled or separable is known to be an NP-hard problem in general, and even the task of detecting entanglement breakdown for a gi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2022-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ac7fb2 |
| _version_ | 1797748457447882752 |
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| author | M A Gavreev A S Mastiukova E O Kiktenko A K Fedorov |
| author_facet | M A Gavreev A S Mastiukova E O Kiktenko A K Fedorov |
| author_sort | M A Gavreev |
| collection | DOAJ |
| description | Quantum technologies require methods for preparing and manipulating entangled multiparticle states. However, the problem of determining whether a given quantum state is entangled or separable is known to be an NP-hard problem in general, and even the task of detecting entanglement breakdown for a given class of quantum states is difficult. In this work, we develop an approach for revealing entanglement breakdown using a machine learning technique, which is known as ‘learning by confusion’. We consider a family of quantum states, which is parameterized such that there is a single critical value dividing states within this family into separate and entangled. We demonstrate the ‘learning by confusion’ scheme allows us to determine the critical value. Specifically, we study the performance of the method for the two-qubit, two-qutrit, and two-ququart entangled state. In addition, we investigate the properties of the local depolarization and the generalized amplitude damping channel in the framework of the confusion scheme. Within our approach and setting the parameterization of special trajectories, we obtain an entanglement-breakdown ‘phase diagram’ of a quantum channel, which indicates regions of entangled (separable) states and the entanglement-breakdown region. Then we extend the way of using the ‘learning by confusion’ scheme for recognizing whether an arbitrary given state is entangled or separable. We show that the developed method provides correct answers for a variety of states, including entangled states with positive partial transpose. We also present a more practical version of the method, which is suitable for studying entanglement breakdown in noisy intermediate-scale quantum devices. We demonstrate its performance using an available cloud-based IBM quantum processor. |
| first_indexed | 2024-03-12T16:05:03Z |
| format | Article |
| id | doaj.art-e1bde8861b2d4c64aa4e1417e0592802 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:05:03Z |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-e1bde8861b2d4c64aa4e1417e05928022023-08-09T14:25:43ZengIOP PublishingNew Journal of Physics1367-26302022-01-0124707304510.1088/1367-2630/ac7fb2Learning entanglement breakdown as a phase transition by confusionM A Gavreev0https://orcid.org/0000-0003-2860-6576A S Mastiukova1https://orcid.org/0000-0002-1268-4257E O Kiktenko2https://orcid.org/0000-0001-5760-441XA K Fedorov3https://orcid.org/0000-0002-4722-3418Russian Quantum Center , Skolkovo, Moscow 143025, Russia; Moscow Institute of Physics and Technology , Dolgoprudny, Moscow Region 141700, RussiaRussian Quantum Center , Skolkovo, Moscow 143025, Russia; Moscow Institute of Physics and Technology , Dolgoprudny, Moscow Region 141700, Russia; Schaffhausen Institute of Technology , Schaffhausen 8200, SwitzerlandRussian Quantum Center , Skolkovo, Moscow 143025, Russia; Moscow Institute of Physics and Technology , Dolgoprudny, Moscow Region 141700, Russia; Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences , Moscow 119991, RussiaRussian Quantum Center , Skolkovo, Moscow 143025, Russia; Schaffhausen Institute of Technology , Schaffhausen 8200, SwitzerlandQuantum technologies require methods for preparing and manipulating entangled multiparticle states. However, the problem of determining whether a given quantum state is entangled or separable is known to be an NP-hard problem in general, and even the task of detecting entanglement breakdown for a given class of quantum states is difficult. In this work, we develop an approach for revealing entanglement breakdown using a machine learning technique, which is known as ‘learning by confusion’. We consider a family of quantum states, which is parameterized such that there is a single critical value dividing states within this family into separate and entangled. We demonstrate the ‘learning by confusion’ scheme allows us to determine the critical value. Specifically, we study the performance of the method for the two-qubit, two-qutrit, and two-ququart entangled state. In addition, we investigate the properties of the local depolarization and the generalized amplitude damping channel in the framework of the confusion scheme. Within our approach and setting the parameterization of special trajectories, we obtain an entanglement-breakdown ‘phase diagram’ of a quantum channel, which indicates regions of entangled (separable) states and the entanglement-breakdown region. Then we extend the way of using the ‘learning by confusion’ scheme for recognizing whether an arbitrary given state is entangled or separable. We show that the developed method provides correct answers for a variety of states, including entangled states with positive partial transpose. We also present a more practical version of the method, which is suitable for studying entanglement breakdown in noisy intermediate-scale quantum devices. We demonstrate its performance using an available cloud-based IBM quantum processor.https://doi.org/10.1088/1367-2630/ac7fb2entanglementmachine learninglearning by confusionphase transitions |
| spellingShingle | M A Gavreev A S Mastiukova E O Kiktenko A K Fedorov Learning entanglement breakdown as a phase transition by confusion New Journal of Physics entanglement machine learning learning by confusion phase transitions |
| title | Learning entanglement breakdown as a phase transition by confusion |
| title_full | Learning entanglement breakdown as a phase transition by confusion |
| title_fullStr | Learning entanglement breakdown as a phase transition by confusion |
| title_full_unstemmed | Learning entanglement breakdown as a phase transition by confusion |
| title_short | Learning entanglement breakdown as a phase transition by confusion |
| title_sort | learning entanglement breakdown as a phase transition by confusion |
| topic | entanglement machine learning learning by confusion phase transitions |
| url | https://doi.org/10.1088/1367-2630/ac7fb2 |
| work_keys_str_mv | AT magavreev learningentanglementbreakdownasaphasetransitionbyconfusion AT asmastiukova learningentanglementbreakdownasaphasetransitionbyconfusion AT eokiktenko learningentanglementbreakdownasaphasetransitionbyconfusion AT akfedorov learningentanglementbreakdownasaphasetransitionbyconfusion |