Digital quantum simulations and quantum error-correction protocols require the application of local gates. We demonstrate such local control in a Sr-88 tweezer array platform by locally shifting the qubit frequency using off-resonant light. This enables precise, highly parallel local Z rotations with low crosstalk. In combination with fast, recoil-free global X rotations, optimized via optimal-control techniques to minimize motional entanglement, this approach allows the local implementation of universal single-qubit gates at rates exceeding 20 kHz. Together with two-qubit operations based on strong Rydberg blockade, we can realize a universal quantum gate set. Equipped with qubit shuttling, our platform opens an exciting frontier for quantum computing, digital quantum simulation, and quantum metrology.
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