Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
University of Chinese Academy of Sciences
| Published: | 2021-06-04, volume 5, page 466 |
| Eprint: | arXiv:2102.01828v2 |
| Doi: | https://doi.org/10.22331/q-2021-06-04-466 |
| Citation: | Quantum 5, 466 (2021). |
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Abstract
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.
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