Realization and Calibration of Continuously Parameterized Two-Qubit Gates on a Trapped-Ion Quantum Processor

Continuously parameterized two-qubit gates are a key feature of state-of-the-art trapped-ion quantum processors as they have favorable error scalings and show distinct improvements in circuit performance over more restricted maximally entangling gatesets. In this work, we provide a comprehensive and pedagogical discussion on how to practically implement these continuously parameterized M{\o}lmer-S{\o}rensen gates on the Quantum Scientific Computing Open User Testbed (QSCOUT), a low-level trapped-ion processor. To generate the arbitrary entangling angles, $\theta$, we simply scale the amplitude of light used to generate the entanglement. However, doing so requires careful consideration of amplifier saturation as well as the variable light shifts that result. As such, we describe a method to calibrate and cancel the dominant fourth-order effects, followed by a dynamic virtual phase advance during the gate to cancel any residual light shifts, and find a linear scaling between $\theta$ and the residual light shift. Once, we have considered and calibrated these effects, we demonstrate performance improvement with decreasing $\theta$. Finally, we describe nuances of hardware control to transform the XX-type interaction of the arbitrary-angle M{\o}lmer-S{\o}rensen gate into a phase-agnostic and crosstalk-mitigating ZZ interaction.