Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus
This work provides a new analytical tool for quantum algorithm developers to predict and avoid barren plateaus in quantum neural network training, which is a significant obstacle for the practical application of quantum machine learning.
This paper proposes a general scheme using the ZX-calculus to analyze the barren plateau phenomenon in quantum neural networks, extending the barren plateaus theorem beyond unitary 2-design circuits. Applying this method to four different quantum neural networks, the authors found that hardware efficient and MPS-inspired ansatze exhibit barren plateaus, while QCNN and tree tensor network ansatze do not.
In this paper, we propose a general scheme to analyze the gradient vanishing phenomenon, also known as 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 ansatz and the tree tensor network ansatz, there exists no barren plateau.