Superconducting quantum circuits provide a versatile platform for studying quantum materials by leveraging precise microwave control and utilizing the tools of circuit quantum electrodynamics(QED). Hybrid circuit devices incorporating novel quantum materials could also lead to new qubit functionalities, such as gate tunability and noise resilience. Here, we report experimental progress towards a transmon-like qubit made with a superconductor-topological insulator-superconductor (S-TI-S) Josephson junction using exfoliated BiSbTeSe2. We present a design that enables us to systematically characterize the hybrid device, from DC transport of the S-TI-S junction, to RF spectroscopy, to full circuit QED control and measurement of the hybrid qubit. In addition, we utilize a high-quality-factor superconducting cavity to characterize material and fabrication-induced losses, thereby guiding our efforts to improve device quality.
Transport measurements are fundamental for understanding condensed matter phenomena, from superconductivity to the fractional quantum Hall effect. Analogously, they can be powerfultools for probing synthetic quantum matter in quantum simulators. Here we demonstrate the measurement of in-situ particle current in a superconducting circuit lattice and apply it to study transport in both coherent and bath-coupled lattices. Our method utilizes controlled tunneling in a double-well potential to map current to on-site density, revealing site-resolved current and current statistics. We prepare a strongly interacting Bose-Hubbard lattice at different lattice fillings, and observe the change in current statistics as the many-body states transition from superfluid to Mott insulator. Furthermore, we explore non-equilibrium current dynamics by coupling the lattice to engineered driven-dissipative baths that serve as tunable particle source and drain. We observe steady-state current in discrete conduction channels and interaction-assisted transport. These results establish a versatile platform to investigate microscopic quantum transport in superconducting circuits.