A weakly-tunable transmon qubit with an optimized shape of the shunted capacitance

An optimized transmon topology is proposed as a base element in a superconducting quantum processor. An analytical formula is obtained for the energy levels of a transmon with three Josephson junctions. It is shown that the three-junction transmon makes it possible to obtain a narrower frequency tunability range in comparison to a two-junction transmon with comparable sizes of Josephson junctions in the structure, that reduces sensitivity to flux noise. Electromagnetic modeling of electric field distribution on technological surfaces is carried out. It is shown that the round shape of the shunted capacitance of the transmon reduces the dielectric losses at the interfaces compared to the most common cross shape.