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We demonstrate high fidelity entangling quantum gates within a chain of fivetrapped ion qubits by optimally shaping optical fields that couple to multiplecollective modes of motion. We individually address qubits with segmentedoptical pulses to construct multipartite entangled states in a programmableway. This approach enables both high fidelity and fast quantum gates that canbe scaled to larger qubit registers for quantum computation and simulation.

Optimal quantum control of multi-mode couplings between trapped ion qubits for scalable entanglement