  Correlation between transmon and its composite Josephson junctions (JJ) plays
an important role in designing new types of superconducting qubits based on
quantum materials. It is desirable to have a type of device that not only
allows exploration for use in quantum information processing but also probing
intrinsic properties in the composite JJs. Here, we construct a flux-tunable 3D
transmon-type superconducting quantum circuit made of graphene as a
proof-of-concept prototype device. This 3D transmon-type device not only
enables coupling to 3D cavities for microwave probes but also permits DC
transport measurements on the same device, providing useful connections between
transmon properties and critical currents associated with JJ's properties. We
have demonstrated how flux-modulation in cavity frequency and DC critical
current can be correlated under the influence of Fraunhofer pattern of JJs in
an asymmetric SQUID. The correlation analysis was further extended to link the
flux-modulated transmon properties, such as flux-tunability in qubit and cavity
frequencies, with SQUID symmetry analysis based on DC measurements. Our study
paves the way towards integrating novel materials for exploration of new types
of quantum devices for future technology while probing underlying physics in
the composite materials.
