Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory
Modeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising aven...
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MDPI AG
2025-04-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/7/2/18 |
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| author | Anshumitra Baul Herbert Fotso Hanna Terletska Ka-Ming Tam Juana Moreno |
| author_facet | Anshumitra Baul Herbert Fotso Hanna Terletska Ka-Ming Tam Juana Moreno |
| author_sort | Anshumitra Baul |
| collection | DOAJ |
| description | Modeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising avenue of research is to combine many-body physics with machine learning for the classification of distinct phases. We present a workflow that synergizes quantum computing, many-body theory, and quantum machine learning (QML) for studying strongly correlated systems. In particular, it can capture a putative quantum phase transition of the stereotypical strongly correlated system, the Hubbard model. Following the recent proposal of the hybrid quantum-classical algorithm for the two-site dynamical mean-field theory (DMFT), we present a modification that allows the self-consistent solution of the single bath site DMFT. The modified algorithm can be generalized for multiple bath sites. This approach is used to generate a database of zero-temperature wavefunctions of the Hubbard model within the DMFT approximation. We then use a QML algorithm to distinguish between the metallic phase and the Mott insulator phase to capture the metal-to-Mott insulator phase transition. We train a recently proposed quantum convolutional neural network (QCNN) and then utilize the QCNN as a quantum classifier to capture the phase transition region. This work provides a recipe for application to other phase transitions in strongly correlated systems and represents an exciting application of small-scale quantum devices realizable with near-term technology. |
| format | Article |
| id | doaj-art-d21c13ecd9e1442d9a0f2cb594f20454 |
| institution | OA Journals |
| issn | 2624-960X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| series | Quantum Reports |
| spelling | doaj-art-d21c13ecd9e1442d9a0f2cb594f204542025-08-20T02:21:57ZengMDPI AGQuantum Reports2624-960X2025-04-01721810.3390/quantum7020018Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field TheoryAnshumitra Baul0Herbert Fotso1Hanna Terletska2Ka-Ming Tam3Juana Moreno4Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USADepartment of Physics, University at Buffalo, Buffalo, NY 14260, USADepartment of Physics and Astronomy, Middle Tennessee State University, Murfreesboro, TN 37132, USADepartment of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USADepartment of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USAModeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising avenue of research is to combine many-body physics with machine learning for the classification of distinct phases. We present a workflow that synergizes quantum computing, many-body theory, and quantum machine learning (QML) for studying strongly correlated systems. In particular, it can capture a putative quantum phase transition of the stereotypical strongly correlated system, the Hubbard model. Following the recent proposal of the hybrid quantum-classical algorithm for the two-site dynamical mean-field theory (DMFT), we present a modification that allows the self-consistent solution of the single bath site DMFT. The modified algorithm can be generalized for multiple bath sites. This approach is used to generate a database of zero-temperature wavefunctions of the Hubbard model within the DMFT approximation. We then use a QML algorithm to distinguish between the metallic phase and the Mott insulator phase to capture the metal-to-Mott insulator phase transition. We train a recently proposed quantum convolutional neural network (QCNN) and then utilize the QCNN as a quantum classifier to capture the phase transition region. This work provides a recipe for application to other phase transitions in strongly correlated systems and represents an exciting application of small-scale quantum devices realizable with near-term technology.https://www.mdpi.com/2624-960X/7/2/18metal insulator transitionMott transitiondynamical mean field theoryquantum machine learningquantum neural networkHubbard model |
| spellingShingle | Anshumitra Baul Herbert Fotso Hanna Terletska Ka-Ming Tam Juana Moreno Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory Quantum Reports metal insulator transition Mott transition dynamical mean field theory quantum machine learning quantum neural network Hubbard model |
| title | Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory |
| title_full | Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory |
| title_fullStr | Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory |
| title_full_unstemmed | Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory |
| title_short | Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory |
| title_sort | quantum classical algorithm for the study of phase transitions in the hubbard model via dynamical mean field theory |
| topic | metal insulator transition Mott transition dynamical mean field theory quantum machine learning quantum neural network Hubbard model |
| url | https://www.mdpi.com/2624-960X/7/2/18 |
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