# Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric

arXiv: https://arxiv.org/abs/2303.13462 · HTML: https://mlsanity.com/paper/2303.13462/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 97 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 30 of 39)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [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)
- [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)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Fisher-Rao Metric, Geometry, and Complexity of Neural Networks](https://mlsanity.com/paper/1711.01530/) (2017)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Capacity and quantum geometry of parametrized quantum circuits](https://mlsanity.com/paper/2102.01659/) (2021)
- [Towards provably efficient quantum algorithms for large-scale machine-learning models](https://mlsanity.com/paper/2303.03428/) (2023)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [Quantum machine learning of large datasets using randomized measurements](https://mlsanity.com/paper/2108.01039/) (2021)
- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
- [Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets](https://mlsanity.com/paper/2007.04900/) (2020)
- [On the statistical complexity of quantum circuits](https://mlsanity.com/paper/2101.06154/) (2021)
- [Learning Unitaries by Gradient Descent](https://mlsanity.com/paper/2001.11897/) (2020)

## Built on by (most cited first, 10 of 10)

- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Double descent in quantum kernel methods](https://mlsanity.com/paper/2501.10077/) (2025)
- [Exponential capacity scaling of classical GANs compared to hybrid latent style-based quantum GANs](https://mlsanity.com/paper/2601.05036/) (2026)
- [Quantum Curriculum Learning](https://mlsanity.com/paper/2407.02419/) (2024)
- [Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise](https://mlsanity.com/paper/2412.11451/) (2024)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)
- [Fisher Information, Training and Bias in Fourier Regression Models](https://mlsanity.com/paper/2510.06945/) (2025)
- [From Reachability to Learnability: Geometric Design Principles for Quantum Neural Networks](https://mlsanity.com/paper/2603.03071/) (2026)
- [A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learning](https://mlsanity.com/paper/2608.24229/) (2026)
- [Measurement-Budget Allocation in Quantum Learning with Finite-Shot Generalization Guarantees](https://mlsanity.com/paper/2608.24891/) (2026)

## Abstract (arXiv)

Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we introduce the data quantum Fisher information metric (DQFIM). It describes the capacity of variational quantum algorithms depending on variational ansatz, training data and their symmetries. We apply the DQFIM to quantify circuit parameters and training data needed to successfully train and generalize. Using the dynamical Lie algebra, we explain how to generalize using a low number of training states. Counter-intuitively, breaking symmetries of the training data can help to improve generalization. Finally, we find that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work provides a useful framework to explore the power of quantum machine learning models.