Diagrammatic Design and Study of Ansätze for Quantum Machine Learning

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 ansatze). This thesis pioneers the use of diagrammatic techniques to reason with QML ansatze. We take commonly used QML ansatze 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 ansatze and also to simplify a class of circuits commonly used in QML.

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