  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.
