Composite pulse sequences, which produce arbitrary predefined rotations of a qubit on the Bloch sphere, are presented. The composite sequences contain up to 17 pulses and can compensate up to 8 orders of experimental errors in the pulse amplitude and the pulse duration. Composite sequences for three basic quantum gates, X (not), Hadamard and arbitrary rotation, are derived. Three classes of composite sequences are presented: one symmetric and two asymmetric. They contain as their lowest members two well-known composite sequences: the three-pulse symmetric SCROFULOUS pulse and the four-pulse asymmetric BB1 pulse, which compensate first- and second-order errors, respectively. The shorter sequences are derived analytically, and the longer ones numerically (instead by nesting and concatenation, as usually done hitherto). Consequently, the composite sequences derived here match or outperform the existing ones in terms of either speed or accuracy, or both. For example, we derive a second-order composite sequence, which is faster (by about 13%) than the famous BB1 sequence. For higher-order sequences, the speedup becomes much more pronounced. This is important for quantum information processing as the sequences derived here provide more options for finding the sweet spot between ultrahigh fidelity and high speed.

中文翻译：

---

超高保真复合旋转量子门

展示了复合脉冲序列，它在布洛赫球体上产生任意预定义的量子位旋转。复合序列包含多达 17 个脉冲，可以补偿多达 8 个数量级的脉冲幅度和脉冲持续时间的实验误差。三个基本量子门的复合序列，X（不), Hadamard 和任意旋转, 推导出来。提出了三类复合序列：一类是对称的，两类是不对称的。它们包含两个众所周知的复合序列作为其最低成员：三脉冲对称 SCROFULOUS 脉冲和四脉冲非对称 BB1 脉冲，它们分别补偿一阶和二阶误差。较短的序列是通过分析推导出来的，而较长的则是通过数值推导出来的（而不是通过嵌套和串联，就像迄今为止通常所做的那样）。因此，此处导出的复合序列在速度或准确性方面匹配或优于现有序列，或两者兼而有之。例如，我们推导出一个二阶复合序列，它比著名的 BB1 序列快（约 13%）。对于高阶序列，加速变得更加明显。