# Absence of Barren Plateaus in Quantum Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2011.02966 · HTML: https://mlsanity.com/paper/2011.02966/

## Key facts

- Cited by 125 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2020.

## Built on by (most cited first, 30 of 125)

- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus](https://mlsanity.com/paper/2102.01828/) (2021)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [Analytic theory for the dynamics of wide quantum neural networks](https://mlsanity.com/paper/2203.16711/) (2022)
- [Symmetric Pruning in Quantum Neural Networks](https://mlsanity.com/paper/2208.14057/) (2022)
- [Quantum anomaly detection in the latent space of proton collision events at the LHC](https://mlsanity.com/paper/2301.10780/) (2023)
- [Quantum Self-Supervised Learning](https://mlsanity.com/paper/2103.14653/) (2021)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Classical-to-quantum convolutional neural network transfer learning](https://mlsanity.com/paper/2208.14708/) (2022)
- [Enhancing Quantum Adversarial Robustness by Randomized Encodings](https://mlsanity.com/paper/2212.02531/) (2022)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)

## Abstract (arXiv)

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 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.