Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction, which requires high-fidelity quantum gates. Analyzing and mitigating gate errors are useful to improve gate fidelity. Here, we demonstrate a simple yet reliable calibration procedure for a high-fidelity controlled-rotation gate in an exchange-always-on Silicon quantum processor, allowing operation above the fault-tolerance threshold of quantum error correction. We find that the fidelity of our uncalibrated controlled-rotation gate is limited by coherent errors in the form of controlled phases and present a method to measure and correct these phase errors. We then verify the improvement in our gate fidelities by randomized benchmark and gate-set tomography protocols. Finally, we use our phase correction protocol to implement a virtual, high-fidelity, controlled-phase gate.

由于相干时间长且与工业铸造工艺兼容，电子自旋量子位是可扩展量子处理器的一个有前途的平台。成熟的量子计算机需要量子纠错，这需要高保真量子门。分析和减轻门错误对于提高门保真度很有用。在这里，我们演示了一种简单而可靠的校准程序，用于交换始终在线的硅量子处理器中的高保真受控旋转门，允许在量子纠错的容错阈值之上运行。我们发现未校准的受控旋转门的保真度受到受控相位形式的相干误差的限制，并提出了一种测量和校正这些相位误差的方法。然后，我们通过随机基准和门组断层扫描协议验证门保真度的改进。最后，我们使用相位校正协议来实现虚拟的高保真受控相位门。