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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Main Authors: Anshumitra Baul, Herbert Fotso, Hanna Terletska, Ka-Ming Tam, Juana Moreno
Format: Article
Language:English
Published: MDPI AG 2025-04-01
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.
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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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