# Generative Quantum Data Embeddings for Supervised Learning

arXiv: https://arxiv.org/abs/2605.30866 · HTML: https://mlsanity.com/paper/2605.30866/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 57 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 21 of 21)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [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)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [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)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Quantum Kernel Alignment with Stochastic Gradient Descent](https://mlsanity.com/paper/2304.09899/) (2023)
- [Enhancing variational quantum state diagonalization using reinforcement learning techniques](https://mlsanity.com/paper/2306.11086/) (2023)
- [Automatic and effective discovery of quantum kernels](https://mlsanity.com/paper/2209.11144/) (2022)
- [A Reinforcement Learning Environment for Directed Quantum Circuit Synthesis](https://mlsanity.com/paper/2401.07054/) (2024)
- [Challenges for Reinforcement Learning in Quantum Circuit Design](https://mlsanity.com/paper/2312.11337/) (2023)
- [Reinforcement learning-based architecture search for quantum machine learning](https://mlsanity.com/paper/2406.02717/) (2024)
- [Hybrid Genetic Optimisation for Quantum Feature Map Design](https://mlsanity.com/paper/2302.02980/) (2023)
- [Understanding Generalization in Quantum Machine Learning with Margins](https://mlsanity.com/paper/2411.06919/) (2024)
- [Synthesis of discrete-continuous quantum circuits with multimodal diffusion models](https://mlsanity.com/paper/2506.01666/) (2025)
- [Early-stage detection of cognitive impairment by hybrid quantum-classical algorithm using resting-state functional MRI time-series](https://mlsanity.com/paper/2405.01554/) (2024)
- [Multi-channel convolutional neural quantum embedding](https://mlsanity.com/paper/2509.22355/) (2025)

## Abstract (arXiv)

Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice. We propose an energy-based generative learning framework that synthesizes gate sequences to optimize embedding structures and refine data-tailored parameters, using a fidelity-based surrogate objective to guide the search toward improved class distinguishability. Empirically, the method improves classification performance across diverse settings, while also revealing datasets where architecture search within the present embedding family yields only limited additional gains. We explain this saturation by deriving bounds on the achievable empirical risk in terms of the Wasserstein distance in the input space, showing that classical data geometry provides an a priori diagnostic for regimes in which substantial gains from embedding optimization are unlikely. The results establish a practically useful and theoretically motivated framework for searching effective quantum data embeddings through generative optimization, with the attainable gains diagnosed through the geometry of the underlying classical data.