# Stochastic noise can be helpful for variational quantum algorithms

arXiv: https://arxiv.org/abs/2210.06723 · HTML: https://mlsanity.com/paper/2210.06723/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 54 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [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)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Gradient Descent Can Take Exponential Time to Escape Saddle Points](https://mlsanity.com/paper/1705.10412/) (2017)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Capacity and quantum geometry of parametrized quantum circuits](https://mlsanity.com/paper/2102.01659/) (2021)
- [Gradient Descent Converges to Minimizers](https://mlsanity.com/paper/1602.04915/) (2016)
- [Analytic theory for the dynamics of wide quantum neural networks](https://mlsanity.com/paper/2203.16711/) (2022)
- [First-order Methods Almost Always Avoid Saddle Points](https://mlsanity.com/paper/1710.07406/) (2017)
- [Adaptive shot allocation for fast convergence in variational quantum algorithms](https://mlsanity.com/paper/2108.10434/) (2021)
- [Laziness, Barren Plateau, and Noise in Machine Learning](https://mlsanity.com/paper/2206.09313/) (2022)
- [Variational Quantum Algorithms for Semidefinite Programming](https://mlsanity.com/paper/2112.08859/) (2021)
- [Bayesian Learning of Parameterised Quantum Circuits](https://mlsanity.com/paper/2206.07559/) (2022)

## Built on by (most cited first, 16 of 16)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [Towards provably efficient quantum algorithms for large-scale machine-learning models](https://mlsanity.com/paper/2303.03428/) (2023)
- [Thermodynamic AI and the fluctuation frontier](https://mlsanity.com/paper/2302.06584/) (2023)
- [SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecture](https://mlsanity.com/paper/2211.12711/) (2022)
- [Method for noise-induced regularization in quantum neural networks](https://mlsanity.com/paper/2410.19921/) (2024)
- [Assessing the Impact of Noise on Quantum Neural Networks: An Experimental Analysis](https://mlsanity.com/paper/2311.14057/) (2023)
- [Image Classification with Rotation-Invariant Variational Quantum Circuits](https://mlsanity.com/paper/2403.15031/) (2024)
- [Enhancing the Trainability of Variational Quantum Circuits with Regularization Strategies](https://mlsanity.com/paper/2405.01606/) (2024)
- [How to find expressible and trainable parameterized quantum circuits?](https://mlsanity.com/paper/2603.14451/) (2026)
- [Escaping Barren Plateaus in Variational Quantum Algorithms Using Negative Learning Rate in Quantum Internet of Things](https://mlsanity.com/paper/2511.22861/) (2025)
- [Quantum End-to-End Learning for Contextual Combinatorial Optimization](https://mlsanity.com/paper/2605.20222/) (2026)
- [Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization](https://mlsanity.com/paper/2307.03884/) (2023)
- [Simplicity Suffices for Parameter Noise Injection in Stochastic Gradient Descent](https://mlsanity.com/paper/2606.12054/) (2026)
- [Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth](https://mlsanity.com/paper/2608.05110/) (2026)
- [A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learning](https://mlsanity.com/paper/2608.24229/) (2026)

## Abstract (arXiv)

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms.