一句话：为纯态量子比特量子计算的 ZW 与 ZX 图示演算给出两个完备公理化。
范畴量子力学将有限维量子理论置于紧致闭范畴中，强调图示推理。该框架下已有两种面向纯态量子比特量子计算的等式图示演算：用于量子比特纠缠分类的 ZW 演算，以及用于抽象描述互补可观察量的 ZX 演算；但二者此前均未给出相对于其模型的完备公理化。本文为这两种演算分别建立完备公理化，表明其公理足以推导相应纯态量子比特模型中的全部等式。该结果强化了 ZW/ZX 演算作为量子计算等式推理基础的地位。
Categorical quantum mechanics places finite-dimensional quantum theory in the context of compact closed categories, with an emphasis on diagrammatic reasoning. In this framework, two equational diagrammatic calculi have been proposed for pure-state qubit quantum computing: the ZW calculus, developed by Coecke, Kissinger and the first author for the purpose of qubit entanglement classification, and the ZX calculus, introduced by Coecke and Duncan to give an abstract description of complementary observables. Neither calculus, however, provided a complete axiomatisation of their model.
DOI 原文 ·
@inproceedings{paperbot4376,
title = {Two complete axiomatisations of pure-state qubit quantum computing},
author = {Amar Hadzihasanovic and Kang Feng Ng and Quanlong Wang},
booktitle = {LICS},
year = {2018},
doi = {10.1145/3209108.3209128}
}