ZX-calculus for the working quantum computer scientist
ZX-calculus for the working quantum computer scientist
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发表时间：
2020-12
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通讯作者：
J. V. D. Wetering
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作者：
J. V. D. Wetering
ZX 微积分是一种用于推理量子计算的图形语言，最近在量子电路优化、表面编码和晶格手术、基于测量的量子计算和量子基础等各个领域的使用有所增加。本评论的前半部分简要介绍了适合熟悉量子计算基础知识的人的 ZX 微积分。这里的目的是让读者对 ZX 微积分足够熟悉，以便他们可以在日常工作中使用它来进行量子电路和状态的小型计算。后面的部分简要概述了 ZX 微积分的文献。我们讨论 Clifford 计算并以图形方式证明 Gottesman-Knill 定理，我们讨论最近引入的 ZX 微积分扩展，它允许方便地推理托夫利门，我们讨论 ZX 微积分最近的完整性定理，该定理表明，原则上，所有关于量子计算的推理都可以使用 ZX 图完成。此外，我们还讨论了 ZX 微积分的分类和代数起源，并讨论了该语言的几种扩展，可以表示混合状态、测量、经典控制和高维量子。
The ZX-calculus is a graphical language for reasoning about quantum computation that has recently seen an increased usage in a variety of areas such as quantum circuit optimisation, surface codes and lattice surgery, measurementbased quantum computation, and quantum foundations. The first half of this review gives a gentle introduction to the ZX-calculus suitable for those familiar with the basics of quantum computing. The aim here is to make the reader comfortable enough with the ZX-calculus that they could use it in their daily work for small computations on quantum circuits and states. The latter sections give a condensed overview of the literature on the ZX-calculus. We discuss Clifford computation and graphically prove the Gottesman-Knill theorem, we discuss a recently introduced extension of the ZX-calculus that allows for convenient reasoning about Toffoli gates, and we discuss the recent completeness theorems for the ZX-calculus that show that, in principle, all reasoning about quantum computation can be done using ZX-diagrams. Additionally, we discuss the categorical and algebraic origins of the ZX-calculus and we discuss several extensions of the language which can represent mixed states, measurement, classical control and higher-dimensional qudits.