Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software level. As such, familiarity with quantum coding is an essential prerequisite for the understanding of current and future quantum computing architectures. In this review, we provide an introductory guide to the theory and implementation of quantum error correction codes. Where possible, fundamental concepts are described using the simplest examples of detection and correction codes, the working of which can be verified by hand. We outline the construction and operation of the surface code, the most widely pursued error correction protocol for experiment. Finally, we discuss issues that arise in the practical implementation of the surface code and other quantum error correction codes.

中文翻译：

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量子纠错：入门指南

量子纠错协议将在量子计算的实现中发挥核心作用；纠错码的选择将影响整个量子计算堆栈，从物理层面的量子位布局到软件层面的门编译策略。因此，熟悉量子编码是理解当前和未来量子计算架构的必要先决条件。在这篇综述中，我们提供了量子纠错码的理论和实现的介绍性指南。在可能的情况下，使用检测和校正代码的最简单示例来描述基本概念，其工作可以手动验证。我们概述了表面代码的构造和操作，这是最广泛采用的实验纠错协议。最后，