论文标题
使用ZXW-Calculus学习量子机器
Quantum Machine Learning using the ZXW-Calculus
论文作者
论文摘要
量子机学习（QML）领域探讨了如何使用量子计算机来更有效地解决机器学习问题。作为混合量子古典算法的应用，它有望在短期内具有潜在的量子优势。在本文中，我们使用ZXW-Calculus来示意分析QML应用所面临的两个关键问题。 首先，我们讨论以计算量子硬件梯度的算法，这些量子对QML进行基于梯度的优化所需的算法。具体而言，我们给出了文献中使用的常见的2和4-期参数转移规则的新图解证据。此外，我们以2N项得出了一种新颖的，广义的参数移位规则，该术语适用于可以用ZXW-Calculus中N参数化的蜘蛛表示的门。此外，据我们所知，我们给了Anselmetti等人的猜想的第一个证据。通过证明无关定理排除了4-期轮班规则的更有效替代方案。 其次，我们使用经验和分析技术分析了用于贫瘠高原的量子Ansätze的梯度景观。具体而言，我们开发了一种工具，该工具会自动计算梯度的方差，并使用它来检测常用量子Ansätze中可能贫瘠的高原。此外，我们正式证明了使用ZXW-Calculus的示意技术选择Ansätze的贫瘠高原存在。
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 ansätze 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 ansätze. Furthermore, we formally prove the existence or absence of barren plateaus for a selection of ansätze using diagrammatic techniques from the ZXW-calculus.
