AI 中文总结
本文扩展了保流的ZX演算重写规则集并证明其对适当形式ZX图间所有保流转换完备，采用保流的电路提取等价方法完成证明。
AI 中文摘要
完备的图形重写规则集可实现量子计算的完全图形化推理，十余年来一直是活跃的研究领域。ZX 演算的诸多近期应用利用了 ZX 图与基于测量的量子计算的单向模型中计算之间的紧密对应关系。在该模型中，各类流属性确保了确定性可实现性；对于 ZX 图而言，这些相同的属性允许将其高效转换为量子电路（该问题在一般情况下被证明是 #P 难的）。因此，保流的 ZX 演算重写规则具有重要研究价值。本文扩展了文献中已有的保流规则集，新增了若干规则并对现有规则进行了扩展。随后证明，所得规则集对于适当形式的 ZX 图之间的所有保流转换是完备的。该证明采用了一种明显保流的电路提取等价方法，即利用仅保流的重写规则，将具有 gflow 的图转换为具有因果流的图。
英文摘要
Complete sets of graphical rewrite rules enable fully graphical reasoning about quantum computations and have been an area of active research for more than a decade. Many recent applications of the ZX-calculus have made use of the close correspondence between ZX-diagrams and computations in the one-way model of measurement-based quantum computation. In this model, various kinds of flow properties ensure deterministic implementability; for ZX-diagrams, these same properties allow efficient translation into quantum circuits (a problem that is known to be #P-hard in general). Therefore, flow-preserving ZX-calculus rewrite rules are of strong interest. Here, we extend the set of flow-preserving rules appearing in the literature with a few new rules and extensions of existing rules. We then show that the resulting rule set is complete for all flow-preserving translations between ZX-diagrams of appropriate form. The proof employs a manifestly flow-preserving equivalent of circuit extraction, where a diagram with gflow is transformed, using only flow-preserving rewrite rules, into a diagram with causal flow.
Comments51 pages
