一句话：为 ZX-图给出通用范式与算法，并证明 Clifford+T 公理对二进角及有理角片段的完备性。
此前 ZX-演算的完备性结果多通过第三方语言 ZW-演算获得，证明优雅但非构造性。本文为包含 Clifford+T 量子力学的任意 ZX-图片段引入通用范式，给出公理化完备的充分条件，并设计达到该范式的算法。作者将结果应用于 Clifford+T 片段、一般 ZX-演算以及有理角片段：证明 Clifford+T 公理对任意二进角片段完备；对其它有理角片段，则证明一条新的消去（cancellation）规则是必要且充分的。该工作为 ZX-演算的有理角完备性提供了构造性框架。
Recent completeness results on the ZX-calculus used a third-party language, namely the ZW-Calculus. As a consequence, these proofs are elegant, but sadly non-constructive. We address this issue in the following. To do so, we first describe a generic normal form for ZX-diagrams in any fragment that contains Clifford+T quantum mechanics. We give sufficient conditions for an axiomatisation to be complete, and an algorithm to reach the normal form. Finally, we apply these results to the Clifford+T fragment and the general ZX-calculus - for which we already know the completeness-, but also for any fragment of rational angles: we show that the axiomatisation for Clifford+T is also complete for any fragment of dyadic angles, and that a simple new rule (called cancellation) is necessary and sufficient otherwise.