  In this paper, we propose a general scheme to analyze the barren plateau
phenomenon in training quantum neural networks with the ZX-calculus. More
precisely, we extend the barren plateaus theorem from unitary 2-design circuits
to any parameterized quantum circuits under certain reasonable assumptions. The
main technical contribution of this paper is representing certain integrations
as ZX-diagrams and computing them with the ZX-calculus. The method is used to
analyze four concrete quantum neural networks with different structures. It is
shown that, for the hardware efficient ansatz and the MPS-inspired ansatz,
there exist barren plateaus, while for the QCNN and the tree tensor network
ansatz, there exists no barren plateau.
