Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus

Understand

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.