Differentiating and Integrating ZX Diagrams


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.

In this paper we give for the first time rules for differentiating arbitrary ZX diagrams and integrating a wide class of ZX diagrams (including quantum circuits), thus paving the way for an analytical version of ZX calculus.

As an example, we apply these new techniques to analyse the barren plateau phenomenon from quantum machine learning.