Coherent noise can be much more damaging than incoherent (probabilistic) noise in the context of quantum error correction. One solution is to use twirling to turn coherent noise into incoherent Pauli channels. In this Article, we show that some of the coherence of the noise channel can actually be used to improve its logical fidelity by simply sandwiching the noise with a chosen pair of Pauli gates, which we call Pauli conjugation. Using the optimal Pauli conjugation, we can achieve a higher logical fidelity than using twirling and doing nothing. We devise a way to search for the optimal Pauli conjugation scheme and apply it to Steane code, 9-qubit Shor code and distance-3 surface code under global coherent \(Z\) noise. The optimal conjugation schemes show improvement in logical fidelity over twirling while the weights of the conjugation gates we need to apply are lower than the average weight of the twirling gates. In our example noise and codes, the concatenated threshold obtained using conjugation is consistently higher than the twirling threshold and can be up to 1.5 times higher than the original threshold where no mitigation is applied. Our simulations show that Pauli conjugation can be robust against gate errors. With the help of logical twirling, the undesirable coherence in the noise channel can be removed and the advantages of conjugation over twirling can persist as we go to multiple rounds of quantum error correction.

在量子误差校正的情况下，相干噪声比不相干（概率）噪声更具破坏性。一种解决方案是使用旋转将相干噪声转换为非相干保利信道。在本文中，我们表明，通过简单地将噪声与选定的一对保利门（我们称为保利共轭）夹在中间，实际上可以使用某些噪声通道的相干性来改善其逻辑保真度。使用最佳保利共轭，我们可以获得比使用旋转而不做任何事情更高的逻辑保真度。我们设计了一种搜索最佳保利共轭方案的方法，并将其应用于全局相干\（Z \）下的Steane码，9比特Shor码和distance-3表面码。噪声。最佳的共轭方案显示了在旋转上逻辑保真度的提高，而我们需要应用的共轭门的权重低于旋转门的平均权重。在我们的示例噪声和代码中，使用共轭获得的串联阈值始终高于旋转阈值，并且可以比未应用缓解措施的原始阈值高1.5倍。我们的仿真表明，保利共轭可以抵抗门误差。借助逻辑旋转，可以消除噪声通道中不希望有的相干性，并且随着我们进行多轮量子误差校正，共轭优于旋转的优势可以继续存在。