Quantum error correction is of crucial importance for fault-tolerant quantum computers. As an essential step towards the implementation of quantum error-correcting codes, quantum non-demolition (QND) measurements are needed to efficiently detect the state of a logical qubit without destroying it. Here we implement QND measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla. Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the ancilla. Repeating this procedure enhances the logical readout fidelity from $75.5\pm 0.3\%$ to $94.5\pm 0.2\%$ after 15 ancilla readouts. In addition, we compare the conventional thresholding method with an improved signal processing method called soft decoding that makes use of analog information in the readout signal to better estimate the state of the logical qubit. We demonstrate that soft decoding leads to a significant reduction in the required number of repetitions when the readout errors become limited by Gaussian noise, for instance in the case of readouts with a low signal-to-noise ratio. These results pave the way for the implementation of quantum error correction with spin qubits in silicon.

中文翻译：

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硅自旋量子位的重复量子不爆测量和软解码

量子纠错对于容错量子计算机至关重要。作为实现量子纠错码的重要步骤，需要进行量子非拆卸（QND）测量，以有效地检测逻辑量子位的状态而不会破坏它。在这里，我们在Si / SiGe两量子位系统中实现QND测量，其中一个量子位用作逻辑量子位，另一个量子位作为辅助。利用两个量子位受控旋转门，将逻辑量子位的状态映射到ancilla上，然后破坏性地读出ancilla。重复此过程可以增强逻辑读出的保真度$75.5\pm 0.3％$ 至 $94.5\pm 0.2％$经过15次ancilla读数。此外，我们将传统的阈值处理方法与改进的信号处理方法（称为软解码）进行了比较，该方法利用读出信号中的模拟信息来更好地估计逻辑量子位的状态。我们证明，当读出错误变得受高斯噪声限制时，例如在信噪比较低的读出情况下，软解码会导致所需重复次数的大幅减少。这些结果为用硅中的自旋量子位实现量子误差校正铺平了道路。