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 asgatemon-like two qubits formed by an epitaxial four-terminal junction. These three configurations provide an 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 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.
We present a new type of transmon split-junction qubit which can be tuned by Meissner screening currents in the adjacent superconducting film electrodes. The best detected relaxationtime was of the order of 50 {\mu}s and the dephasing time about 70 {\mu}s. The achieved period of oscillation with magnetic field was much smaller than in usual SQUID-based transmon qubits, thus a strong effective field amplification has been realized. This Meissner qubit allows an efficient coupling to superconducting vortices. We present a quantitative analysis of the radiation-free energy relaxation in qubits coupled to Abrikosov vortices. The observation of coherent quantum oscillations provides strong evidence that vortices can exist in coherent quantum superpositions of different position states. According to our suggested model, the wave function collapse is defined by Caldeira-Leggett dissipation associated with viscous motion of the vortex cores.