Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail. The most important feature of GST, compared to older state and process tomography protocols, is that it is $\textit{calibration-free}$. GST does not rely on pre-calibrated state preparations and measurements. Instead, it characterizes all the operations in a $\textit{gate set}$ simultaneously and self-consistently, relative to each other. Long sequence GST can estimate gates with very high precision and efficiency, achieving Heisenberg scaling in regimes of practical interest. In this paper, we cover GST's intellectual history, the techniques and experiments used to achieve its intended purpose, data analysis, gauge freedom and fixing, error bars, and the interpretation of gauge-fixed estimates of gate sets. Our focus is fundamental mathematical aspects of GST, rather than implementation details, but we touch on some of the foundational algorithmic tricks used in the $\texttt{pyGSTi}$ implementation.

中文翻译：

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门组断层扫描

门组断层扫描 (GST) 是一种协议，用于对量子计算处理器上的逻辑操作（门）进行详细的预测表征。GST 的早期版本出现在 2012-13 年左右，从那时起，它被改进、演示并用于大量实验。本文全面详细地介绍了 GST 的基础。与旧的状态和过程断层扫描协议相比，GST 最重要的特点是它是 $\textit{calibration-free}$。GST 不依赖于预先校准的状态准备和测量。相反，它同时且自洽地描述了 $\textit{gate set}$ 中的所有操作，并且彼此相关。长序列 GST 可以以非常高的精度和效率估计门，在实际感兴趣的范围内实现海森堡缩放。在本文中，我们涵盖了 GST 的思想史、用于实现其预期目的的技术和实验、数据分析、规范自由度和固定、误差条以及对门集的规范固定估计的解释。我们的重点是 GST 的基本数学方面，而不是实现细节，但我们会触及 $\texttt{pyGSTi}$ 实现中使用的一些基本算法技巧。