Quantum Error Mitigation (QEM) enables the extraction of high-quality results from the presently-available noisy quantum computers. In this approach, the effect of the noise on observables of interest can be mitigated using multiple measurements without additional hardware overhead. Unfortunately, current QEM techniques are limited to weak noise or lack scalability. In this work, we introduce a QEM method termed ‘Adaptive KIK’ that adapts to the noise level of the target device, and therefore, can handle moderate-to-strong noise. The implementation of the method is experimentally simple — it does not involve any tomographic information or machine-learning stage, and the number of different quantum circuits to be implemented is independent of the size of the system. Furthermore, we have shown that it can be successfully integrated with randomized compiling for handling both incoherent as well as coherent noise. Our method handles spatially correlated and time-dependent noise which enables us to run shots over the scale of days or more despite the fact that noise and calibrations change in time. Finally, we discuss and demonstrate why our results suggest that gate calibration protocols should be revised when using QEM. We demonstrate our findings in the IBM quantum computers and through numerical simulations.

量子误差缓解（QEM）能够从目前可用的噪声量子计算机中提取高质量的结果。在这种方法中，可以使用多次测量来减轻噪声对感兴趣的可观测值的影响，而无需额外的硬件开销。不幸的是，当前的 QEM 技术仅限于弱噪声或缺乏可扩展性。在这项工作中，我们引入了一种称为“自适应 KIK”的 QEM 方法，该方法可适应目标设备的噪声水平，因此可以处理中等到强的噪声。该方法的实现在实验上很简单——它不涉及任何断层扫描信息或机器学习阶段，并且要实现的不同量子电路的数量与系统的大小无关。此外，我们还表明，它可以成功地与随机编译集成，以处理不相干和相干噪声。我们的方法处理空间相关和时间相关的噪声，这使我们能够在数天或更长时间的范围内运行镜头，尽管噪声和校准会随时间变化。最后，我们讨论并论证了为什么我们的结果表明在使用 QEM 时应该修改门校准协议。我们在 IBM 量子计算机中并通过数值模拟展示了我们的发现。