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

We consider gatemon qubits based on superconductor-semiconductor-superconductor Josephson junctions, whose properties can be tuned (via conduction channel transparency) with an electrostatic gate. Our theoretical approach builds on previous work, which focused on Andreev-level physics in the high-transparency regime, and aims to establish a rigorous physical correspondence with conventional transmon physics at low transparency, while remaining consistent with recent experimental data. Using our approach we investigate the qubit's full level structure, selection rules, and coherence properties, and the corresponding implications for qubit manipulation and measurement via a capacitively coupled superconducting resonator.