Utilizing transmon qudits for quantum simulation of the Fermi-Hubbard model

Abstract

The Fermi-Hubbard model is instrumental in shedding light on the complexities of many strongly correlated phenomena in condensed matter physics. Although exact solutions for the Fermi-Hubbard model are attainable in specific settings, quantum simulations offer the possible exploration of this model within more complex scenarios. In this work, we introduce a novel approach to simulating the Fermi-Hubbard model utilizing transmon qudits. Leveraging on the inherent properties of qudits, we develop an effective map between the fermionic degrees of the Fermi-Hubbard model, to a single four-level system (i.e., a ququart), thus reducing the complexity of encoding and simulating the many-body systems. While our approach is generic and hardware agnostic, we showcase the power of this method by utilizing superconducting transmons and their native gates as our qudits. Our results reveal the advantages of qudits in quantum simulations, providing valuable insights into the underlying physics of strongly correlated systems and establishing a new paradigm for the study of quantum many-body systems using higher-dimensional computational subspaces.