ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain unreachable with current ZX techniques. Here we elevate ZX to an analytical perspective by realising differentiation and integration entirely within the framework of ZX-calculus. We explicitly illustrate the new analytic framework of ZX-calculus by applying it in context of quantum machine learning for the analysis of barren plateaus.

中文翻译：

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区分 ZX 图并将其与量子机器学习的应用程序集成


ZX 演算已被证明是量子技术的有用工具，具有广泛的成功应用。这些应用程序中的大多数都是代数性质的。但是，涉及差异化和集成的其他任务仍然无法使用当前的 ZX 技术来完成。在这里，我们通过在 ZX 演算的框架内实现微分和积分，将 ZX 提升到分析视角。我们通过在量子机器学习的背景下应用ZX演算来明确说明ZX演算的新分析框架，以分析贫瘠的高原。