论文标题
工作量子计算机科学家的ZX-Calculus
ZX-calculus for the working quantum computer scientist
论文作者
论文摘要
ZX-Calculus是一种用于推理量子计算的图形语言，最近在各种领域（例如量子电路优化，表面代码和晶格手术，基于测量的量子计算和量子基础）中使用了增加的用法。这篇评论的上半年对ZX-Calculus进行了轻柔的介绍，适合那些熟悉量子计算基础的人。这里的目的是使读者对ZX-Calculus足够舒适，他们可以在日常工作中使用它来用于量子电路和状态的小型计算。后一部分给出了有关ZX-Calculus文献的凝结概述。我们讨论Clifford计算并以图形方式证明了Gottesman-Knill定理，我们讨论了最近引入的ZX-Calculus扩展的扩展，允许有关Toffoli Gates的方便推理，我们讨论了ZX-Calculus的最新完整定理，该理论表明，这些ZX-Calculus均表明，所有这些都可以使用Quantum Computitation使用ZX-Diagrams进行ZX-DIAGRAMS。此外，我们讨论了ZX-Calculus的分类和代数起源，并讨论了该语言的几种扩展，这些扩展可以代表混合状态，测量，经典控制和更高维度。
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, measurement-based 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.
