Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory

• Published in: Quantum reports Vol. 7; no. 2; p. 18
• Main Authors: Baul, Anshumitra, Fotso, Herbert, Terletska, Hanna, Tam, Ka-Ming, Moreno, Juana
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.06.2025
• Subjects: Algorithms; Approximation; Artificial neural networks; Computers; Correlation; dynamical mean field theory; Hilbert space; Hubbard model; Machine learning; Mean field theory; metal insulator transition; Methods; Mott transition; Neural networks; Numerical analysis; Phase transitions; Quantum computers; Quantum computing; quantum machine learning; quantum neural network; Simulation; Wave functions
• ISSN: 2624-960X; 2624-960X
• DOI: 10.3390/quantum7020018

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.