# Entangled Datasets for Quantum Machine Learning

arXiv: https://arxiv.org/abs/2109.03400 · HTML: https://mlsanity.com/paper/2109.03400/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 90 references that are in the map.
- First posted on arXiv 8 Sep 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [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)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [ProteinNet: a standardized data set for machine learning of protein structure](https://mlsanity.com/paper/1902.00249/) (2019)
- [Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions](https://mlsanity.com/paper/1811.00414/) (2018)
- [Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets](https://mlsanity.com/paper/2007.04900/) (2020)
- [Machine Learning Phase Transitions with a Quantum Processor](https://mlsanity.com/paper/1906.10155/) (2019)
- [Generalization in Quantum Machine Learning: a Quantum Information Perspective](https://mlsanity.com/paper/2102.08991/) (2021)

## Built on by (most cited first, 27 of 27)

- [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)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [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)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [A Survey on Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead](https://mlsanity.com/paper/2310.10315/) (2023)
- [QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design](https://mlsanity.com/paper/2410.07961/) (2024)
- [Quantum neural networks form Gaussian processes](https://mlsanity.com/paper/2305.09957/) (2023)
- [Scalable Quantum Neural Networks for Classification](https://mlsanity.com/paper/2208.07719/) (2022)
- [What can we learn from quantum convolutional neural networks?](https://mlsanity.com/paper/2308.16664/) (2023)
- [Transition Role of Entangled Data in Quantum Machine Learning](https://mlsanity.com/paper/2306.03481/) (2023)
- [Experimentally validated quantum-secure federated learning over a multi-user quantum network](https://mlsanity.com/paper/2501.12709/) (2025)
- [Variational Denoising for Variational Quantum Eigensolver](https://mlsanity.com/paper/2304.00549/) (2023)
- [QuFeX: Quantum feature extraction module for hybrid quantum-classical deep neural networks](https://mlsanity.com/paper/2501.13165/) (2025)
- [MNISQ: A Large-Scale Quantum Circuit Dataset for Machine Learning on/for Quantum Computers in the NISQ era](https://mlsanity.com/paper/2306.16627/) (2023)
- [Quantum continual learning of quantum data realizing knowledge backward transfer](https://mlsanity.com/paper/2203.14032/) (2022)
- [Identification of quantum entanglement with Siamese convolutional neural networks and semi-supervised learning](https://mlsanity.com/paper/2210.07410/) (2022)
- [A Post-Training Approach for Mitigating Overfitting in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2309.01829/) (2023)
- [Microscopy is All You Need](https://mlsanity.com/paper/2210.06526/) (2022)
- [Computable Model-Independent Bounds for Adversarial Quantum Machine Learning](https://mlsanity.com/paper/2411.06863/) (2024)
- [Learning from imperfect quantum data via unsupervised domain adaptation with classical shadows](https://mlsanity.com/paper/2603.28294/) (2026)
- [Ravines in quantum cost landscapes: opportunities for improved VQA predictions](https://mlsanity.com/paper/2607.01329/) (2026)

## Abstract (arXiv)

High-quality, large-scale datasets have played a crucial role in the development and success of classical machine learning. Quantum Machine Learning (QML) is a new field that aims to use quantum computers for data analysis, with the hope of obtaining a quantum advantage of some sort. While most proposed QML architectures are benchmarked using classical datasets, there is still doubt whether QML on classical datasets will achieve such an advantage. In this work, we argue that one should instead employ quantum datasets composed of quantum states. For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement. We first show how a quantum neural network can be trained to generate the states in the NTangled dataset. Then, we use the NTangled dataset to benchmark QML models for supervised learning classification tasks. We also consider an alternative entanglement-based dataset, which is scalable and is composed of states prepared by quantum circuits with different depths. As a byproduct of our results, we introduce a novel method for generating multipartite entangled states, providing a use-case of quantum neural networks for quantum entanglement theory.