The Mølmer-Sørensen (MS) gate is a two-qubit controlled-phase gate in ion traps that is highly valued due to its ability to preserve the motional state of the ions. However, its fidelity is obstructed by errors affecting the motion of the ions as well as the rotation of the qubits. In this work, we propose an amplitude-modulated composite MS gate, which features high fidelity, robust to gate timing, detuning, and coupling errors and is also tolerant of ac Stark shifts and drifting detuning errors. With the proposed amplitude-modulated composite sequence, we maintain gate infidelities below ${10}^{-3}$ even under simultaneous detuning, timing, and coupling errors as large as 10–15%, outperforming both standard and multitone MS gate implementations. The physical origin of this improvement is due to a separation of the error channels: the amplitude modulation suppresses residual spin-motion displacement (hence reducing sensitivity to detuning and timing imperfections), while the composite phase schedule cancels the dominant over- and under-rotation of the entangling phase produced by coupling miscalibration.

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• Coherent control
• Quantum control
• Quantum gates
• Quantum information with trapped ions
• Quantum optics
• Quantum protocols
• Quantum state transfer
• Trapped ions