# Enhancing the Trainability of Variational Quantum Circuits with Regularization Strategies

arXiv: https://arxiv.org/abs/2405.01606 · HTML: https://mlsanity.com/paper/2405.01606/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 57 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Provable Benefit of Orthogonal Initialization in Optimizing Deep Linear Networks](https://mlsanity.com/paper/2001.05992/) (2020)
- [Regularizing Deep Neural Networks by Noise: Its Interpretation and Optimization](https://mlsanity.com/paper/1710.05179/) (2017)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Escaping Saddle Points with Adaptive Gradient Methods](https://mlsanity.com/paper/1901.09149/) (2019)
- [Generative quantum machine learning via denoising diffusion probabilistic models](https://mlsanity.com/paper/2310.05866/) (2023)
- [On the saddle point problem for non-convex optimization](https://mlsanity.com/paper/1405.4604/) (2014)
- [VSQL: Variational Shadow Quantum Learning for Classification](https://mlsanity.com/paper/2012.08288/) (2020)
- [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)
- [Stochastic noise can be helpful for variational quantum algorithms](https://mlsanity.com/paper/2210.06723/) (2022)
- [Avoiding Barren Plateaus with Classical Deep Neural Networks](https://mlsanity.com/paper/2205.13418/) (2022)
- [Quantum algorithms for escaping from saddle points](https://mlsanity.com/paper/2007.10253/) (2020)
- [Mitigating barren plateaus of variational quantum eigensolvers](https://mlsanity.com/paper/2205.13539/) (2022)
- [Hierarchical Learning for Quantum ML: Novel Training Technique for Large-Scale Variational Quantum Circuits](https://mlsanity.com/paper/2311.12929/) (2023)
- [Quark: A Gradient-Free Quantum Learning Framework for Classification Tasks](https://mlsanity.com/paper/2210.01311/) (2022)
- [Robust Node Representation Learning via Graph Variational Diffusion Networks](https://mlsanity.com/paper/2312.10903/) (2023)
- [Mitigating Noise-Induced Gradient Vanishing in Variational Quantum Algorithm Training](https://mlsanity.com/paper/2111.13209/) (2021)

## 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)
- [Large Language Models Can Help Mitigate Barren Plateaus in Quantum Neural Networks](https://mlsanity.com/paper/2502.13166/) (2025)

## Abstract (arXiv)

In the era of noisy intermediate-scale quantum (NISQ), variational quantum circuits (VQCs) have been widely applied in various domains, demonstrating the potential advantages of quantum circuits over classical models. Similar to classic models, VQCs can be optimized by various gradient-based methods. However, the optimization may get stuck in barren plateaus initially or trapped in saddle points during training. These gradient-related issues can severely impact the trainability of VQCs. In this work, we propose a strategy that regularizes model parameters with prior knowledge of the training data and Gaussian noise diffusion. We conduct ablation studies to verify the effectiveness of our strategy across four public datasets and demonstrate that our method can improve the trainability of VQCs against the above-mentioned gradient issues.