  Microwave-driven trapped ion logic gates offer a promising avenue for
advancing beyond laser-based logic operations. In future microwave-based
operations, however, the joule heat produced by large microwave currents
flowing through narrow microwave electrodes would potentially hinder
improvements in gate speed and fidelity. Moreover, scalability, particularly in
cryogenic trapped ion systems, is impeded by the excessive joule heat. To
address these challenges, we present a novel approach: superconducting surface
trap chips that integrate high-$Q$ microwave resonators with large current
capacities. Utilizing sub-ampere microwave currents in superconducting Nb
resonators, we generate substantial magnetic field gradients with significantly
reduced losses compared to conventional metal chips. By harnessing the high $Q$
factors of superconducting resonators, we propose a power-efficient two-qubit
gate scheme capable of achieving a sub-milliwatt external microwave input power
at a gate Rabi frequency of 1 kHz.
