Controlled-Z gate for transmon qubits coupled by semiconductor junctions

We analyze the coupling of two qubits via an epitaxial semiconducting junction. In particular, we consider three configurations that include pairs of transmons or gatemons as well as gatemonlike two qubits formed by an epitaxial four-terminal junction. These three configurations provide electrical control of the interaction between the qubits by applying voltage to a metallic gate near the semiconductor junction and can be utilized to naturally realize a controlled-Z gate (CZ). We calculate the fidelity and timing for such a CZ gate. We demonstrate that in the absence of decoherence, the CZ gate can be performed under 50 ns with gate error below 10(-4).