Demonstration of Mølmer–Sørensen Gates Robust to +/-10 kHz Motional Frequency Error*

Two of the most significant barriers to trapped ion quantum computing are scalability and susceptibility of the entangling gates to technical noise. In this work, we make substantial advancement towards addressing these issues by designing and testing a Mølmer-Sørensen (MS) entangling gate that is robust against a dominant noise source – variation in the motional mode frequencies. Our gate uses a simple Gaussian pulse shape that exponentially suppresses displacement (loop closure) errors. This gives us the freedom to tackle sensitivity of the gate's spin-spin rotation angle to detuning error by operating at a frequency that balances the contribution of multiple motional modes. The resulting 'balanced Gaussian' MS gate is broadly robust to motional frequency offset errors, and we experimentally demonstrate <1% drop in fidelity over a +/-10 kHz range in frequency error. Further, we numerically study the scalability of our design and find the gate retains its robustness against frequency error on chains of up to 33 ions.