# Entanglement Induced Barren Plateaus

arXiv: https://arxiv.org/abs/2010.15968 · HTML: https://mlsanity.com/paper/2010.15968/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2020.

## Built on by (most cited first, 30 of 101)

- [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)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [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)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [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)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [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)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [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)
- [QSAN: A Near-term Achievable Quantum Self-Attention Network](https://mlsanity.com/paper/2207.07563/) (2022)
- [Symmetric Pruning in Quantum Neural Networks](https://mlsanity.com/paper/2208.14057/) (2022)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [On the Sample Complexity of Quantum Boltzmann Machine Learning](https://mlsanity.com/paper/2306.14969/) (2023)
- [On fundamental aspects of quantum extreme learning machines](https://mlsanity.com/paper/2312.15124/) (2023)
- [Enhancing Quantum Adversarial Robustness by Randomized Encodings](https://mlsanity.com/paper/2212.02531/) (2022)
- [Optimal training of variational quantum algorithms without barren plateaus](https://mlsanity.com/paper/2104.14543/) (2021)
- [BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2204.13751/) (2022)

## Abstract (arXiv)

We argue that an excess in entanglement between the visible and hidden units in a Quantum Neural Network can hinder learning. In particular, we show that quantum neural networks that satisfy a volume-law in the entanglement entropy will give rise to models not suitable for learning with high probability. Using arguments from quantum thermodynamics, we then show that this volume law is typical and that there exists a barren plateau in the optimization landscape due to entanglement. More precisely, we show that for any bounded objective function on the visible layers, the Lipshitz constants of the expectation value of that objective function will scale inversely with the dimension of the hidden-subsystem with high probability. We show how this can cause both gradient descent and gradient-free methods to fail. We note that similar problems can happen with quantum Boltzmann machines, although stronger assumptions on the coupling between the hidden/visible subspaces are necessary. We highlight how pretraining such generative models may provide a way to navigate these barren plateaus.