Robust Two-Qubit Geometric Phase Gates using Amplitude and Frequency Ramping

Entangling operations that are robust to environmental noise or miscalibrations are fundamental to scalable quantum systems across experimental platforms. Geometric phase gates are a widely employed method to realize trapped ion entanglement by coupling the ions’ spin to their shared motion, displacing the motion in phase space such that the internal states acquire a state-dependent geometric phase. Historically, the fidelity of the operation is sensitive to the shared motional mode, requiring experimentally time-consuming ground-state cooling sequences and precise calibration of mode frequencies.  

We present a method for entangling trapped atomic ions whose fidelity is robust to both the motional occupation and to drifts or frequency offsets of the motional mode addressed by the gate. We achieve this by adiabatically ramping both the amplitude of the gate drive creating the state-dependent force (SDF) and the detuning between the motional mode and the SDF. Using these ramped control fields, we demonstrate Bell state fidelities in excess of 0.99 that are independent of motional occupation for up to 10 phonons and robust to offsets in the mode frequency. We perform the entangling operations on two ⁴⁰Ca⁺ ions, but use a driving scheme that is well suited for mixed-species entanglement and quantum logic operations, which is the next focus of our work.