Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Barren Plateaus in Quantum Neural Networks

Marco Cerezo de la Roca, Akira Sone, Kunal Sharma, Tyler J. Volkoff, Łukasz Cincio, Patrick J. Coles

Published Mar 18, 2021• 1 citation
OpenAlex

Related papers

The barren plateaus of quantum neural networks: review, taxonomy and trends

Han Qi, Lei Wang, Hongsheng Zhu +2 more

Quantum Information Processing•Dec 11, 2023•25 citations

Trainability of Quantum Neural Networks: Barren Plateaus and Scalability

Patrick J. Coles

Bulletin of the American Physical Society•Mar 19, 2021•0 citations

Defeating Barren Plateaus with Task-Aligned Symmetry

Ruipeng Xing, Yanan Li, Zhen Shang +3 more

Barren plateaus -- the exponential vanishing of gradients -- are a fundamental obstacle to training scalable quantum neural networks. Whether they arise in quantum recurrent neural networks (QRNNs), a natural architecture for sequential data, remains a pressing question. Here we show that the decisive ingredient for trainability in QRNNs is not the recurrent circuit topology per se, but enforcing time-translation symmetry through parameter sharing across time steps. We prove that, without parameter sharing, QRNNs suffer from barren plateaus, with gradient variance decaying exponentially with sequence length. Imposing parameter sharing across time steps fundamentally alters this scaling, transforming it into a polynomial dependence and thereby suppressing the barren plateau. Numerical simulations corroborate these analytical predictions. By rigorously showing how time-translation symmetry suppresses barren plateaus and enhances learning capability in QRNNs, our work establishes task-aligned symmetry as a constructive resolution to the expressivity-trainability tension in quantum neural networks.

quant-pharXiv:2607.12100•Jul 15, 2026•0 citations

Impact of barren plateaus countermeasures on the quantum neural network capacity to learn

Jacob L. Cybulski, Thanh Thi Nguyen

Quantum Information Processing•Dec 14, 2023•10 citations

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

Chen Zhao, Xiao-Shan Gao

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.

arXiv:2102.01828•Quantum•Jun 4, 2021•84 citations

Absence of Barren Plateaus in Quantum Convolutional Neural Networks

Arthur Chalom Pesah, Marco Cerezo, Samson Wang +3 more

Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data.But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures.Recently, quantum convolutional neural networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features.In this work, we rigorously analyze the gradient scaling for the parameters in the QCNN architecture.We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus.This result provides an analytical guarantee for the trainability of randomly initialized QCNNs, which highlights QCNNs as being trainable under random initialization unlike many other QNN architectures.To derive our results, we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts.Finally, we perform numerical simulations to verify our analytical results.

arXiv:2011.02966•Physical Review X•Oct 15, 2021•343 citations
Barren plateaus -- the exponential vanishing of gradients -- are a fundamental obstacle to training scalable quantum neural networks. Whether they arise in quantum recurrent neural networks (QRNNs), a natural architecture for sequential data, remains a pressing question. Here we show that the decisive ingredient for trainability in QRNNs is not the recurrent circuit topology per se, but enforcing time-translation symmetry through parameter sharing across time steps. We prove that, without parameter sharing, QRNNs suffer from barren plateaus, with gradient variance decaying exponentially with sequence length. Imposing parameter sharing across time steps fundamentally alters this scaling, transforming it into a polynomial dependence and thereby suppressing the barren plateau. Numerical simulations corroborate these analytical predictions. By rigorously showing how time-translation symmetry suppresses barren plateaus and enhances learning capability in QRNNs, our work establishes task-aligned symmetry as a constructive resolution to the expressivity-trainability tension in quantum neural networks.
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.
Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data.But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures.Recently, quantum convolutional neural networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features.In this work, we rigorously analyze the gradient scaling for the parameters in the QCNN architecture.We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus.This result provides an analytical guarantee for the trainability of randomly initialized QCNNs, which highlights QCNNs as being trainable under random initialization unlike many other QNN architectures.To derive our results, we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts.Finally, we perform numerical simulations to verify our analytical results.