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ZX-calculus has proved to be a useful tool for quantum technology with a widerange of successful applications. Most of these applications are of analgebraic nature. However, other tasks that involve differentiation andintegration remain unreachable with current ZX techniques. Here we elevate ZXto an analytical perspective by realising differentiation and integrationentirely within the framework of ZX-calculus. We explicitly illustrate the newanalytic framework of ZX-calculus by applying it in context of quantum machinelearning for the analysis of barren plateaus.

Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning