Almost every quantum circuit is built with two-qubit gates in the current stage, which are crucial to the quantum computing in any platform. The entangling gates based on Mølmer-Sørensen schemes are widely exploited in the trapped-ion system, with the utilization of the collective motional modes of ions and two laser-controlled internal states, which are served as qubits. The key to realize high-fidelity and robust gates is the minimization of the entanglement between the qubits and the motional modes under various sources of errors after the gate operation. In this work, we propose an efficient numerical method to search high-quality solutions for phase-modulated pulses. Instead of directly optimizing a cost function, which contains the fidelity and the robustness of the gates, we convert the problem to the combination of linear algebra and the solution to quadratic equations. Once a solution with the gate fidelity of 1 is found, the laser power can be further reduced while searching on the manifold where the fidelity remains 1. Our method largely overcomes the problem of the convergence and is shown to be effective up to 60 ions, which suffices the need of the gate design in current trapped-ion experiments.

中文翻译：

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捕获离子长链中高保真相位调制门的有效数值方法

目前几乎每个量子电路都构建了两个量子位门，这对任何平台的量子计算都至关重要。基于 Mølmer-Sørensen 方案的纠缠门在俘获离子系统中得到广泛利用，利用离子的集体运动模式和两个激光控制的内部状态，用作量子位。实现高保真和鲁棒门的关键是在门操作后的各种误差源下最小化量子位和运动模式之间的纠缠。在这项工作中，我们提出了一种有效的数值方法来搜索相位调制脉冲的高质量解。不是直接优化包含门的保真度和鲁棒性的成本函数，我们将问题转换为线性代数和二次方程解的组合。一旦找到门保真度为 1 的解，在保真度保持为 1 的流形上搜索时，可以进一步降低激光功率。我们的方法在很大程度上克服了收敛问题，并证明对 60 个离子有效，满足了目前离子阱实验中门设计的需要。