Reaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.

达到高速，高保真度的量子位操作需要对基础脉冲的形状进行精确控制。对于弱非谐波系统，例如超导跨界量子位，短门导致泄漏到计算子空间外部的状态。通过开环最佳控制设计的控制脉冲可以减少此类泄漏。但是，模型不正确会严重限制此类脉冲的可用性。我们实施了一个闭环优化，该优化基于根据Clifford门构建的成本函数的测量值同时调整所有控制参数。我们直接优化数字化控制脉冲的每个采样点的幅度和相位。因此，我们充分利用了脉冲生成电子设备的功能，并创建了一个4.16 ns的单量子位脉冲，其保真度为99.76％，泄漏为0.044％。