We take commonly used QML ans\”{a}tze and convert them to diagrammatic form . We give a full description of how these gates commute . Weverage a combinatorial description of the interaction between CNOTs and phasegadgets to analyse a periodicity phenomenon in layered ans\’tze . We also use combinatorially description of interaction between the interaction of CNOT . and phase gadgets to analyse periodicity . phenomenon . We use diagrammatic techniques tosimplify a class of circuits commonly used in QML .

Author(s) : Richie Yeung

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Keywords : ans - tze - diagrammatic - description - interaction -

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