# Mitigating Noise-Induced Gradient Vanishing in Variational Quantum Algorithm Training

arXiv: https://arxiv.org/abs/2111.13209 · HTML: https://mlsanity.com/paper/2111.13209/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 25 Nov 2021.

## Builds on (most cited first, 8 of 8)

- [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)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits](https://mlsanity.com/paper/2001.00550/) (2020)

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

- [Enhancing the Trainability of Variational Quantum Circuits with Regularization Strategies](https://mlsanity.com/paper/2405.01606/) (2024)
- [Large Language Models Can Help Mitigate Barren Plateaus in Quantum Neural Networks](https://mlsanity.com/paper/2502.13166/) (2025)

## Abstract (arXiv)

Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the algorithm increases. Previous work cannot handle the gradient vanishing induced by the inevitable noise effects on realistic quantum hardware. In this paper, we propose a novel training scheme to mitigate such noise-induced gradient vanishing. We first introduce a new cost function of which the gradients are significantly augmented by employing traceless observables in truncated subspace. We then prove that the same minimum can be reached by optimizing the original cost function with the gradients from the new cost function. Experiments show that our new training scheme is highly effective for major variational quantum algorithms of various tasks.