# SAFE Quantum Machine Learning with Variational Quantum Classifiers

arXiv: https://arxiv.org/abs/2605.16067 · HTML: https://mlsanity.com/paper/2605.16067/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 15 May 2026.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [nnU-Net Revisited: A Call for Rigorous Validation in 3D Medical Image Segmentation](https://mlsanity.com/paper/2404.09556/) (2024)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Adversarial Robustness Toolbox v1.0.0](https://mlsanity.com/paper/1807.01069/) (2018)
- [Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group](https://mlsanity.com/paper/1901.08428/) (2019)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Recurrent Orthogonal Networks and Long-Memory Tasks](https://mlsanity.com/paper/1602.06662/) (2016)
- [HiFuse: Hierarchical Multi-Scale Feature Fusion Network for Medical Image Classification](https://mlsanity.com/paper/2209.10218/) (2022)
- [Advanced Tumor Segmentation in Medical Imaging: An Ensemble Approach for BraTS 2023 Adult Glioma and Pediatric Tumor Tasks](https://mlsanity.com/paper/2403.09262/) (2024)
- [Deep learning trends for focal brain pathology segmentation in MRI](https://mlsanity.com/paper/1607.05258/) (2016)
- [Radio Signal Classification by Adversarially Robust Quantum Machine Learning](https://mlsanity.com/paper/2312.07821/) (2023)
- [Hybrid Quantum Neural Networks with Amplitude Encoding: Advancing Recovery Rate Predictions](https://mlsanity.com/paper/2501.15828/) (2025)

## Built on by (most cited first, 1 of 1)

- [QBFF: Deep Quantum Bottleneck for Automatic Speaker Verification Anti-Spoofing](https://mlsanity.com/paper/2610.16390/) (2026)

## Abstract (arXiv)

We propose a variational quantum classifier operating on high dimensional deep representations via amplitude encoding, stabilized by a learnable classical pre encoding layer.By combining normalized amplitude embeddings with bounded quantum observables, the resulting model induces a structured and smooth hypothesis class with controlled sensitivity to input variations. Model reliability is assessed using SAFE-AI metrics derived from the Cramer von Mises divergence, enabling consistent evaluation across accuracy, robustness, and explainability dimensions. Empirical results show that the proposed quantum model provides competitive predictive performance compared with strong classical baselines while exhibiting a more balanced SAFE reliability profile, with improved robustness to noise and stability under structured feature removal. These findings suggest that variational quantum circuits offer a principled mechanism for stability oriented SAFE learning in safety critical settings.