# Quantum Embedding Search for Quantum Machine Learning

arXiv: https://arxiv.org/abs/2105.11853 · HTML: https://mlsanity.com/paper/2105.11853/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 65 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 19 of 19)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [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)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [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)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Quantum-enhanced machine learning](https://mlsanity.com/paper/1610.08251/) (2016)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [The Expressive Power of Parameterized Quantum Circuits](https://mlsanity.com/paper/1810.11922/) (2018)

## Built on by (most cited first, 7 of 7)

- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [Quantum Convolutional Neural Networks with Interaction Layers for Classification of Classical Data](https://mlsanity.com/paper/2307.11792/) (2023)
- [Several fitness functions and entanglement gates in quantum kernel generation](https://mlsanity.com/paper/2309.03307/) (2023)
- [A novel feature selection method based on quantum support vector machine](https://mlsanity.com/paper/2311.17646/) (2023)
- [Empowering Credit Scoring Systems with Quantum-Enhanced Machine Learning](https://mlsanity.com/paper/2404.00015/) (2024)
- [Neural Architecture Search Algorithms for Quantum Autoencoders](https://mlsanity.com/paper/2509.15451/) (2025)
- [Neural Manifolds and Cognitive Consistency: A New Approach to Memory Consolidation in Artificial Systems](https://mlsanity.com/paper/2503.01867/) (2025)

## Abstract (arXiv)

This paper introduces a novel quantum embedding search algorithm (QES, pronounced as "quest"), enabling search for optimal quantum embedding design for a specific dataset of interest. First, we establish the connection between the structures of quantum embedding and the representations of directed multi-graphs, enabling a well-defined search space. Second, we instigate the entanglement level to reduce the cardinality of the search space to a feasible size for practical implementations. Finally, we mitigate the cost of evaluating the true loss function by using surrogate models via sequential model-based optimization. We demonstrate the feasibility of our proposed approach on synthesis and Iris datasets, which empirically shows that found quantum embedding architecture by QES outperforms manual designs whereas achieving comparable performance to classical machine learning models.