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

Simulating quantum many-body systems is believed to be one of the most promising applications of 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. In this paper, we propose 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 classical-quantum 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 easily 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 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.