# Barren plateaus are amplified by the dimension of qudits

arXiv: https://arxiv.org/abs/2405.08190 · HTML: https://mlsanity.com/paper/2405.08190/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Quantum Data Encoding: A Comparative Analysis of Classical-to-Quantum Mapping Techniques and Their Impact on Machine Learning Accuracy](https://mlsanity.com/paper/2311.10375/) (2023)
- [Hybrid quantum convolutional neural networks model for COVID-19 prediction using chest X-Ray images](https://mlsanity.com/paper/2102.06535/) (2021)
- [Natural Evolutionary Strategies for Variational Quantum Computation](https://mlsanity.com/paper/2012.00101/) (2020)
- [A hybrid quantum-classical neural network with deep residual learning](https://mlsanity.com/paper/2012.07772/) (2020)
- [Avoiding Barren Plateaus with Classical Deep Neural Networks](https://mlsanity.com/paper/2205.13418/) (2022)
- [The quantum cost function concentration dependency on the parametrization expressivity](https://mlsanity.com/paper/2301.06883/) (2023)
- [Evolution strategies: Application in hybrid quantum-classical neural networks](https://mlsanity.com/paper/2205.08059/) (2022)
- [Restricting to the chip architecture maintains the quantum neural network accuracy](https://mlsanity.com/paper/2212.14426/) (2022)
- [Quantum neural network with ensemble learning to mitigate barren plateaus and cost function concentration](https://mlsanity.com/paper/2402.06026/) (2024)

## Built on by (most cited first, 2 of 2)

- [Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Survey](https://mlsanity.com/paper/2407.17706/) (2024)
- [Single-Qudit Quantum Neural Networks for Multiclass Classification](https://mlsanity.com/paper/2503.09269/) (2025)

## Abstract (arXiv)

Variational Quantum Algorithms (VQAs) have emerged as pivotal strategies for attaining quantum advantage in diverse scientific and technological domains, notably within Quantum Neural Networks. However, despite their potential, VQAs encounter significant obstacles, chief among them being the vanishing gradient problem, commonly referred to as barren plateaus. In this article, through meticulous analysis, we demonstrate that existing literature implicitly suggests the intrinsic influence of qudit dimensionality on barren plateaus. To instantiate these findings, we present numerical results that exemplify the impact of qudit dimensionality on barren plateaus. Therefore, despite the proposition of various error mitigation techniques, our results call for further scrutiny about their efficacy in the context of VQAs with qudits.