Abstract: 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.
Authors: Chen Zhao, Xiao-Shan Gao (Chinese Academy of Sciences)