Integrated ${}^9$Be${}^{+}$ multi-qubit gate device for the ion-trap quantum computer

We demonstrate the experimental realization of a two-qubit M{\o}lmer-S{\o}rensen gate on a magnetic field-insensitive hyperfine transition in ${}^9$Be${}^{+}$ ions using microwave-near fields emitted by a single microwave conductor embedded in a surface-electrode ion trap. The design of the conductor was optimized to produce a high oscillating magnetic field gradient at the ion position. The measured gate fidelity is determined to be $98.2\pm 1.2\mathrm{\%}$ and is limited by technical imperfections, as is confirmed by a comprehensive numerical error analysis. The conductor design can potentially simplify the implementation of multi-qubit gates and represents a self-contained, scalable module for entangling gates within the quantum CCD architecture for an ion-trap quantum computer.