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- W4307207871 abstract "The field of quantum machine learning (QML) explores how quantum computers can be used to more efficiently solve machine learning problems. As an application of hybrid quantum-classical algorithms, it promises a potential quantum advantages in the near term. In this thesis, we use the ZXW-calculus to diagrammatically analyse two key problems that QML applications face. First, we discuss algorithms to compute gradients on quantum hardware that are needed to perform gradient-based optimisation for QML. Concretely, we give new diagrammatic proofs of the common 2- and 4-term parameter shift rules used in the literature. Additionally, we derive a novel, generalised parameter shift rule with 2n terms that is applicable to gates that can be represented with n parametrised spiders in the ZXW-calculus. Furthermore, to the best of our knowledge, we give the first proof of a conjecture by Anselmetti et al. by proving a no-go theorem ruling out more efficient alternatives to the 4-term shift rule. Secondly, we analyse the gradient landscape of quantum ansatze for barren plateaus using both empirical and analytical techniques. Concretely, we develop a tool that automatically calculates the variance of gradients and use it to detect likely barren plateaus in commonly used quantum ansatze. Furthermore, we formally prove the existence or absence of barren plateaus for a selection of ansatze using diagrammatic techniques from the ZXW-calculus." @default.
- W4307207871 created "2022-10-30" @default.
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- W4307207871 date "2022-10-18" @default.
- W4307207871 modified "2023-10-14" @default.
- W4307207871 title "Quantum Machine Learning using the ZXW-Calculus" @default.
- W4307207871 doi "https://doi.org/10.48550/arxiv.2210.11523" @default.
- W4307207871 hasPublicationYear "2022" @default.
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