# Constructing Optimal Noise Channels for Enhanced Robustness in Quantum Machine Learning

arXiv: https://arxiv.org/abs/2404.16417 · HTML: https://mlsanity.com/paper/2404.16417/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 25 Apr 2024.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [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)
- [Quantum Differential Privacy: An Information Theory Perspective](https://mlsanity.com/paper/2202.10717/) (2022)
- [Benchmarking Adversarially Robust Quantum Machine Learning at Scale](https://mlsanity.com/paper/2211.12681/) (2022)
- [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)
- [Predominant Aspects on Security for Quantum Machine Learning: Literature Review](https://mlsanity.com/paper/2401.07774/) (2024)
- [A unifying framework for differentially private quantum algorithms](https://mlsanity.com/paper/2307.04733/) (2023)
- [Quantum Neural Networks under Depolarization Noise: Exploring White-Box Attacks and Defenses](https://mlsanity.com/paper/2311.17458/) (2023)

## Built on by (most cited first, 5 of 5)

- [Adversarial Robustness Guarantees for Quantum Classifiers](https://mlsanity.com/paper/2405.10360/) (2024)
- [Certifiably Robust Encoding Schemes](https://mlsanity.com/paper/2408.01200/) (2024)
- [Detecting underdetermination in parameterized quantum circuits](https://mlsanity.com/paper/2504.03315/) (2025)
- [Quantum Support Vector Regression for Robust Anomaly Detection](https://mlsanity.com/paper/2505.01012/) (2025)
- [Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth](https://mlsanity.com/paper/2608.05110/) (2026)

## Abstract (arXiv)

With the rapid advancement of Quantum Machine Learning (QML), the critical need to enhance security measures against adversarial attacks and protect QML models becomes increasingly evident. In this work, we outline the connection between quantum noise channels and differential privacy (DP), by constructing a family of noise channels which are inherently ε-DP: (α, γ)-channels. Through this approach, we successfully replicate the ε-DP bounds observed for depolarizing and random rotation channels, thereby affirming the broad generality of our framework. Additionally, we use a semi-definite program to construct an optimally robust channel. In a small-scale experimental evaluation, we demonstrate the benefits of using our optimal noise channel over depolarizing noise, particularly in enhancing adversarial accuracy. Moreover, we assess how the variables α and γ affect the certifiable robustness and investigate how different encoding methods impact the classifier's robustness.