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We report the design, fabrication, and characterization of a cryogenic iontrap system for the implementation of quantum logic driven by near-fieldmicrowaves. The trap incorporates an on-chip microwave resonator with anelectrode geometry designed to null the microwave field component that couplesdirectly to the qubit, while giving a large field gradient for drivingentangling logic gates. We map the microwave field using a single $^{43}$Ca$^+$ion, and measure the ion trapping lifetime and motional mode heating rates forone and two ions.

Cryogenic ion trap system for high-fidelity near-field microwave-driven quantum logic