Controlled–Z gate for two transmon qubits coupled by semiconductor wire

We propose a realization of controlled–Z (CZ) gate for two transmon qubits connected by an epitaxial semiconductor wire. This arrangement provides an electrical control of the interaction between the qubits by applying a voltage to a metallic gate near the wire. We calculate the gate fidelity and gate time for the CZ gate. We demonstrate that in the absence of decoherence, the CZ gate can be performed under 50ns with gate error below 10^-4. We also evaluate the CZ gate for two gatemon qubits coupled by a semiconductor wire and for a system of two gatemon–like qubits formed by a single semiconductor H-junction.