# Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise

arXiv: https://arxiv.org/abs/2412.11451 · HTML: https://mlsanity.com/paper/2412.11451/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 94 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 30 of 44)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [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)
- [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)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Generalization Error in Deep Learning](https://mlsanity.com/paper/1808.01174/) (2018)
- [Generalization bounds for deep learning](https://mlsanity.com/paper/2012.04115/) (2020)
- [Capacity and quantum geometry of parametrized quantum circuits](https://mlsanity.com/paper/2102.01659/) (2021)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [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)

## Built on by (most cited first, 1 of 1)

- [Quantum Machine Unlearning: Foundations, Mechanisms, and Taxonomy](https://mlsanity.com/paper/2511.00406/) (2025)

## Abstract (arXiv)

Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the generalizability of quantum circuit models. Designing robust quantum machine learning models under noise requires a principled understanding of complexity and generalization, extending beyond classical capacity measures. This study investigates the generalization properties of parameterized quantum machine learning models under the influence of noise. We present a data-dependent generalization bound grounded in the quantum Fisher information matrix. We leverage statistical learning theory to relate the parameter space volumes and training sizes to estimate the generalization capability of the trained model. We provide a structured characterization of complexity in quantum models by integrating local parameter neighborhoods and effective dimensions defined through quantum Fisher information matrix eigenvalues. We also analyze the tightness of the bound and discuss the tradeoff between model expressiveness and generalization performance.