Gatemon qubits with superconductor-semiconductor-superconductor junctions: transition from high transparency to low transparency

We consider a superconductor-semiconductor-superconductor Josephson junction embedded in a general superconducting circuit environment, whose properties can be tuned (via conduction channel transparency and Andreev-level separation) with an electrostatic gate. Our work is based on a self-consistent approach, which focuses on the Andreev-level physics of a semiconductor quantum dot coupled via tunneling to superconducting leads, and we aim to establish a rigorous physical correspondence with conventional Josephson junction physics at low transparency. Using our approach, we investigate the qubit's full level structure, selection rules, and coherence properties. Gatemon manipulation and measurement via a capacitively coupled superconducting resonator are also discussed.