一句话：提出费米子ZW演算，为费米子量子计算提供图解语言，并证明其等式公理化完备。
本文针对费米子量子计算（FQC）提出一种弦图式语言——费米子 ZW 演算。作者先定义费米子线路模型，给出演算的基本组件及其解释，并说明 FQC 中的主要物理门如何由图表示；随后列出一组公理并推导额外等式。通过将任意图重写为规范形的过程，证明这些公理构成了以有限多个局域费米模式（LFM）系统为对象、保奇偶或反奇偶映射为态射、张量积为幺半积的幺半范畴的完备等式公理化。文中还以费米子 Mach-Zehnder 干涉仪的统计量计算为例，并给出双轨编码的图解处理。
We introduce the fermionic ZW calculus, a string-diagrammatic language for fermionic quantum computing (FQC). After defining a fermionic circuit model, we present the basic components of the calculus, together with their interpretation, and show how the main physical gates of interest in FQC can be represented in our language. We then list our axioms, and derive some additional equations. We prove that the axioms provide a complete equational axiomatisation of the monoidal category whose objects are systems of finitely many local fermionic modes (LFMs), with maps that preserve or reverse the parity of states, and the tensor product as monoidal product. We achieve this through a procedure that rewrites any diagram in a normal form. As an example, we show how the statistics of a fermionic Mach-Zehnder interferometer can be calculated in the diagrammatic language. We conclude by giving a diagrammatic treatment of the dual-rail encoding, a standard method in optical quantum computing used to perform universal quantum computation.
@article{paperbot759,
title = {A diagrammatic calculus of fermionic quantum circuits},
author = {Giovanni de Felice and Amar Hadzihasanovic and Kang Feng Ng},
journal = {Logical Methods in Computer Science},
volume = {Volume 15, Issue 3},
year = {2019},
doi = {10.23638/lmcs-15(3:26)2019}
}