Engineering quantum devices requires reliable characterization of the quantum system, including qubits, quantum operations (also known as instruments) and the quantum noise. Recently, quantum gate set tomography (GST) has emerged as a powerful technique for self-consistently describing quantum states, gates, and measurements. However, non-Markovian correlations between the quantum system and environment impact the reliability of GST. To address this, we propose a self-consistent operational framework called instrument set tomography (IST) for non-Markovian GST. Based on the stochastic quantum process, the instrument set describes instruments and system-environment (SE) correlations. We introduce a linear inversion IST (LIST) to describe instruments and SE correlations without physical constraints. The disharmony of linear relationships between instruments is detected. Furthermore, we propose a physically constrained statistical method based on the maximum likelihood estimation for IST (MLE-IST) with adjustable dimensions. MLE-IST shows significant flexibility in adapting to different types of devices, such as noisy intermediate-scale quantum (NISQ) devices, by adjusting the model and constraints. Experimental results demonstrate the effectiveness and necessity of simultaneously describing instruments and SE correlations. Specifically, the LIST and MLE-IST obtains significant improvement on average square error reduction in the imperfect implemented simulations by orders of −23.77 and −6.21, respectively, compared to their comparative methods. Remarkably, real-chip experiments indicate that a polynomial number of parameters with respect to the Markovian order are sufficient to characterize non-Markovian quantum noise in current NISQ devices. Consequently, IST provides an essential and self-consistent framework for characterizing, benchmarking, and developing quantum devices in terms of the instrument set.

中文翻译：

---

非马尔可夫量子门组层析成像

工程量子设备需要对量子系统进行可靠的表征，包括量子位、量子操作（也称为仪器）和量子噪声。最近，量子门组层析成像 (GST) 已成为一种强大的技术，用于自洽地描述量子态、门和测量。然而，量子系统和环境之间的非马尔可夫相关性会影响 GST 的可靠性。为了解决这个问题，我们提出了一个自洽的操作框架，称为非马尔可夫 GST 仪器组断层扫描 (IST)。基于随机量子过程，仪器集描述了仪器和系统环境（SE）的相关性。我们引入线性反演 IST (LIST) 来描述仪器和 SE 相关性，而无需物理约束。检测仪器之间线性关系的不和谐。此外，我们提出了一种基于可调整维度的 IST (MLE-IST) 最大似然估计的物理约束统计方法。通过调整模型和约束，MLE-IST 在适应不同类型的设备（例如噪声中尺度量子 (NISQ) 设备）方面表现出显着的灵活性。实验结果证明了同时描述仪器和SE相关性的有效性和必要性。具体来说，与比较方法相比，LIST 和 MLE-IST 在不完美实现的模拟中，平均平方误差减少量分别显着提高了 -23.77 和 -6.21。值得注意的是，真实芯片实验表明，关于马尔可夫阶数的多项式参数足以表征当前 NISQ 器件中的非马尔可夫量子噪声。因此，IST 提供了一个基本且自洽的框架，用于在仪器组方面表征、基准测试和开发量子设备。