The performance of a quantum information processor depends on the precise control of phases introduced into the system during quantum gate operations. As the number of operations increases with the complexity of a computation, the phases of gates at different locations and different times must be controlled, which can be challenging for optically-driven operations. We circumvent this issue by demonstrating an entangling gate between two trapped atomic ions that is insensitive to the optical phases of the driving fields, while using a common master reference clock for all coherent qubit operations. Such techniques may be crucial for scaling to large quantum information processors in many physical platforms.
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