ZX演算为工作的量子计算机科学家
ZX-calculus for the working quantum computer scientist
摘要：
ZX演算是一种用于量子计算推理的图形语言，最近在各种领域中的使用越来越多，例如量子线路优化，表面码和晶格手术，基于测量的量子计算和量子基础。这篇评论的前半部分对ZX演算进行了温和的介绍，适合那些熟悉量子计算基础的人。这里的目的是让读者对ZX演算足够熟悉，以便他们可以在日常工作中使用它来进行量子线路和状态的小型计算。后面的部分给出了关于ZX演算的文献的简要概述。我们讨论克利福德计算和图形证明Gottesman-Knill定理，我们讨论了最近推出的扩展ZX演算，允许方便的推理Toffoli门，我们讨论了最近的完备性定理的ZX演算，表明，在原则上，所有的推理量子计算可以使用ZX图。此外，我们讨论的ZX演算的范畴和代数的起源，我们讨论了几个扩展的语言，可以代表混合状态，测量，经典控制和高维qudits。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
