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.

翻译：ZX演算已被证明是量子技术领域中一种有效的工具，具有广泛且成功的应用案例。这些应用大多属于代数性质。然而，涉及微分与积分的其他任务在当前ZX技术中仍无法实现。本文通过完全在ZX演算框架内实现微分与积分，将ZX提升至分析视角。我们通过在量子机器学习背景下应用该框架分析贫瘠高原现象，具体阐释了ZX演算的新分析框架。