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Generating quantum entanglement in large systems on time scales much shorterthan the coherence time is key to powerful quantum simulation and computation.Trapped ions are among the most accurately controlled and best isolated quantumsystems with low-error entanglement gates operated via the vibrational motionof a few-ion crystal within tens of microseconds. To exceed the level ofcomplexity tractable by classical computers the main challenge is to realisefast entanglement operations in large ion crystals. The strong dipole-dipoleinteractions in polar molecule and Rydberg atom systems allow much fasterentangling gates, yet stable state-independent confinement comparable withtrapped ions needs to be demonstrated in these systems. Here, we combine thebenefits of these approaches: we report a $700\,\mathrm{ns}$ two-ion entanglinggate which utilises the strong dipolar interaction between trapped Rydberg ionsand produce a Bell state with $78\%$ fidelity. The sources of gate error areidentified and a total error below $0.2\%$ is predicted forexperimentally-achievable parameters. Furthermore, we predict that residualcoupling to motional modes contributes $\sim 10^{-4}$ gate error in a large ioncrystal of 100 ions. This provides a new avenue to significantly speed up andscale up trapped ion quantum computers and simulators.

Sub-microsecond entangling gate between trapped ions via Rydberg interaction