Circuit quantum electrodynamics has proven to be a powerful tool to probe mesoscopic effects in hybrid systems and is used in several quantum computing (QC) proposals that require a transmon qubit able to operate in strong magnetic fields. To address this we integrate monolayer graphene Josephson junctions into microwave frequency superconducting circuits to create graphene based transmons. Using dispersive microwave spectroscopy we resolve graphene's characteristic band dispersion and observe coherent electronic interference effects confirming the ballistic nature of our graphene Josephson junctions. We show that the monoatomic thickness of graphene renders the device insensitive to an applied magnetic field, allowing us to perform energy level spectroscopy of the circuit in a parallel magnetic field of 1 T, an order of magnitude higher than previous studies. These results establish graphene based superconducting circuits as a promising platform for QC and the study of mesoscopic quantum effects that appear in strong magnetic fields.

The current-phase relation (CPR) of a Josephson junction (JJ) determines how the supercurrent evolves with the superconducting phase difference across the junction. Knowledge of the CPR is essential in order to understand the response of a JJ to various external parameters. Despite the rising interest in ultraclean encapsulated graphene JJs, the CPR of such junctions remains unknown. Here, we use a fully gate-tunable graphene superconducting quantum intereference device (SQUID) to determine the CPR of ballistic graphene JJs. Each of the two JJs in the SQUID is made with graphene encapsulated in hexagonal boron nitride. By independently controlling the critical current of the JJs, we can operate the SQUID either in a symmetric or asymmetric configuration. The highly asymmetric SQUID allows us to phase-bias one of the JJs and thereby directly obtain its CPR. The CPR is found to be skewed, deviating significantly from a sinusoidal form. The skewness can be tuned with the gate voltage and oscillates in antiphase with Fabry-Pérot resistance oscillations of the ballistic graphene cavity. We compare our experiments with tight-binding calculations that include realistic graphene-superconductor interfaces and find a good qualitative agreement.