# Certifiably Robust Encoding Schemes

arXiv: https://arxiv.org/abs/2408.01200 · HTML: https://mlsanity.com/paper/2408.01200/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 2 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Quantum Adversarial Machine Learning](https://mlsanity.com/paper/2001.00030/) (2019)
- [Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework](https://mlsanity.com/paper/2002.09169/) (2020)
- [Optimal Provable Robustness of Quantum Classification via Quantum Hypothesis Testing](https://mlsanity.com/paper/2009.10064/) (2020)
- [Certified Robustness of Quantum Classifiers against Adversarial Examples through Quantum Noise](https://mlsanity.com/paper/2211.00887/) (2022)
- [An exponentially-growing family of universal quantum circuits](https://mlsanity.com/paper/2212.00736/) (2022)
- [Enhancing Quantum Adversarial Robustness by Randomized Encodings](https://mlsanity.com/paper/2212.02531/) (2022)
- [Quantum Adversarial Learning for Kernel Methods](https://mlsanity.com/paper/2404.05824/) (2024)
- [Quantum Neural Networks under Depolarization Noise: Exploring White-Box Attacks and Defenses](https://mlsanity.com/paper/2311.17458/) (2023)
- [Constructing Optimal Noise Channels for Enhanced Robustness in Quantum Machine Learning](https://mlsanity.com/paper/2404.16417/) (2024)
- [Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness](https://mlsanity.com/paper/2305.00472/) (2023)
- [Discrete Randomized Smoothing Meets Quantum Computing](https://mlsanity.com/paper/2408.00895/) (2024)

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

- [Adversarial Robustness of Partitioned Quantum Classifiers](https://mlsanity.com/paper/2502.20403/) (2025)

## Abstract (arXiv)

Quantum machine learning uses principles from quantum mechanics to process data, offering potential advances in speed and performance. However, previous work has shown that these models are susceptible to attacks that manipulate input data or exploit noise in quantum circuits. Following this, various studies have explored the robustness of these models. These works focus on the robustness certification of manipulations of the quantum states. We extend this line of research by investigating the robustness against perturbations in the classical data for a general class of data encoding schemes. We show that for such schemes, the addition of suitable noise channels is equivalent to evaluating the mean value of the noiseless classifier at the smoothed data, akin to Randomized Smoothing from classical machine learning. Using our general framework, we show that suitable additions of phase-damping noise channels improve empirical and provable robustness for the considered class of encoding schemes.