Given the rising popularity of quantum machine learning (QML), it is important to develop techniques that effectively simplify commonly adopted families of parameterised quantum circuits (commonly known as ans\"{a}tze). This thesis pioneers the use of diagrammatic techniques to reason with QML ans\"{a}tze. We take commonly used QML ans\"{a}tze and convert them to diagrammatic form and give a full description of how these gates commute, making the circuits much easier to analyse and simplify. Furthermore, we leverage a combinatorial description of the interaction between CNOTs and phase gadgets to analyse a periodicity phenomenon in layered ans\"{a}tze and also to simplify a class of circuits commonly used in QML.

中文翻译：

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量子机器学习的图解设计与研究

鉴于量子机器学习（QML）的日益普及，开发有效简化常用的参数化量子电路族（通常称为ans'tze）的技术非常重要。 QML ans \“ {a} tze的原因。我们采用常用的QML ans \“ {a} tze并将其转换为图表形式，并对这些门的通勤方式进行了完整描述，从而使电路更易于分析和简化。此外，我们利用组合描述来描述CNOT和相位小工具，用于分析分层响应中的周期性现象，并简化QML中常用的一类电路。