Robust quantum gates between trapped ions using shaped pulses

• We present a systematic method to optimize the shape of the pulses to decouple qubits from intermediary motional modes.
• Our optimized scheme can be applied to both the ultrafast gate and fast gate.
• Our optimized scheme can suppress the dominant source of infidelity to arbitrary order.
• When the number of trapped ions increase, the number of needed segments increases slowly.

We improve two existing entangling gate schemes between trapped ion qubits immersed in a large linear crystal. Based on the existing two-qubit gate schemes by applying segmented forces on the individually addressed qubits, we present a systematic method to optimize the shapes of the forces to suppress the dominant source of infidelity. The spin-dependent forces in the scheme can be from periodic photon kicks or from continuous optical pulses. The entangling gates are fast, robust, and have high fidelity. They can be used to implement scalable quantum computation and quantum simulation.