Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning
This work addresses a limitation in quantum technology tools for tasks like optimization in quantum machine learning, though it appears incremental as it extends existing ZX-calculus methods.
The authors tackled the problem of performing differentiation and integration within ZX-calculus, which was previously unreachable, by developing an analytical framework and applied it to analyze barren plateaus in quantum machine learning, demonstrating its utility in this context.
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.