Experimental realization of a two-qubit entangling transport gate with trapped ions

We perform a two-qubit entangling Mølmer-Sørensen gate by transporting two trapped 40Ca+ ions through a stationary,  global laser beam. Waveform resampling dynamically compensates for observed nonuniformities in velocity to produce a constant qubit-frequency Doppler shift during transport. We analyze two different methods for Stark shift compensation: (1) applying a constant frequency offset to the gate beams or (2) finely adjusting the transport waveform sampling so that the associated Doppler shifts dynamically cancel the Stark shifts. We compare the performance of this gate to stationary gates performed in the same system and show that the transport gate provides a natural Gaussian intensity ramp which should minimize off-resonant coupling. This represents the first demonstration of a two-ion entangling gate mediated with ion transport rather than via optical switching, and it could relax the requirements on optical-pulse timing precision and on the optical power needed for parallel gate operations.