# Generalization in Quantum Machine Learning: a Quantum Information Perspective

arXiv: https://arxiv.org/abs/2102.08991 · HTML: https://mlsanity.com/paper/2102.08991/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 61 references that are in the map.
- First posted on arXiv 17 Feb 2021.

## Builds on (most cited first, 15 of 15)

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [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)
- [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)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [The Conditional Entropy Bottleneck](https://mlsanity.com/paper/2002.05379/) (2020)
- [The Learnability of Unknown Quantum Measurements](https://mlsanity.com/paper/1501.00559/) (2015)
- [Quantum-enhanced barcode decoding and pattern recognition](https://mlsanity.com/paper/2010.03594/) (2020)
- [Statistical Limits of Supervised Quantum Learning](https://mlsanity.com/paper/2001.10477/) (2020)

## Built on by (most cited first, 11 of 11)

- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [Structural risk minimization for quantum linear classifiers](https://mlsanity.com/paper/2105.05566/) (2021)
- [The dilemma of quantum neural networks](https://mlsanity.com/paper/2106.04975/) (2021)
- [Classical-to-quantum convolutional neural network transfer learning](https://mlsanity.com/paper/2208.14708/) (2022)
- [Fock State-enhanced Expressivity of Quantum Machine Learning Models](https://mlsanity.com/paper/2107.05224/) (2021)
- [Accelerating variational quantum algorithms with multiple quantum processors](https://mlsanity.com/paper/2106.12819/) (2021)
- [Optimizing Quantum Convolutional Neural Network Architectures for Arbitrary Data Dimension](https://mlsanity.com/paper/2403.19099/) (2024)
- [Quantum Artificial Intelligence for Mission-Critical Systems: Foundations, Architectural Elements, and Future Directions](https://mlsanity.com/paper/2511.09884/) (2025)

## Abstract (arXiv)

Quantum classification and hypothesis testing are two tightly related subjects, the main difference being that the former is data driven: how to assign to quantum states ρ(x) the corresponding class c (or hypothesis) is learnt from examples during training, where x can be either tunable experimental parameters or classical data "embedded" into quantum states. Does the model generalize? This is the main question in any data-driven strategy, namely the ability to predict the correct class even of previously unseen states. Here we establish a link between quantum machine learning classification and quantum hypothesis testing (state and channel discrimination) and then show that the accuracy and generalization capability of quantum classifiers depend on the (R'enyi) mutual informations I(C:Q) and I2(X:Q) between the quantum state space Q and the classical parameter space X or class space C. Based on the above characterization, we then show how different properties of Q affect classification accuracy and generalization, such as the dimension of the Hilbert space, the amount of noise, and the amount of neglected information from X via, e.g., pooling layers. Moreover, we introduce a quantum version of the Information Bottleneck principle that allows us to explore the various tradeoffs between accuracy and generalization. Finally, in order to check our theoretical predictions, we study the classification of the quantum phases of an Ising spin chain, and we propose the Variational Quantum Information Bottleneck (VQIB) method to optimize quantum embeddings of classical data to favor generalization.