Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optimal provable robustness of quantum classification via quantum hypothesis testing

Maurice Weber, Nana Liu, Bo Li, Ce Zhang, Zhikuan Zhao

Published May 21, 2021• 24 citations
Publisher

Abstract

Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.

DOI
10.3929/ethz-b-000488397

Related papers

Optimal provable robustness of quantum classification via quantum hypothesis testing

Maurice Weber, Nana Liu, Bo Li +2 more

Abstract Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.

arXiv:2009.10064•npj Quantum Information•May 21, 2021•43 citations

Towards Robust Quantum Machine Learning

Saeefa Rubaiyet Nowmi, Jesus Lopez, Md Mahmudul Alam Imon +3 more

Quantum Machine Learning (QML) fuses quantum computing with machine learning to address complex tasks with potential speedups over classical methods. While QML models such as variational quantum classifiers (QVC), quantum multilayer perceptron(QMLP) models and quantum convolutional neural networks (QCNN) have demonstrated promise in applications like image recognition and malware classification, they remain vulnerable to adversarial threats. Inspired by the vulnerabilities in classical ML, this work systematically investigates how attacks-ranging from training-time poisoning and inferencetime evasion (e.g., quantum versions of FGSM and PGD) to deployment-time trigger attacks-manifest in quantum circuits. We explore how classical adversarial strategies adapt to quantum models through parameterized encodings, hybrid architectures, and probabilistic outputs. The poster evaluates different quantum classifiers under adversarial settings, comparing their robustness, trainability, and resilience to perturbations. Defense mechanisms such as randomized encoding, engineered noise channels, and quantum adversarial training are analyzed in relation to specific threat types. In addition, we assess how quantum models behave differently than classical counterparts under attack, and how quantum-specific design constraints can either exacerbate or mitigate these effects. Our ultimate goal is to define and construct robust QML systems that are both theoretically sound and practically secure. By synthesizing results across multiple QML architectures and threat models, this work provides actionable insight into the development of resilient quantum classifiers, paving the way toward trustworthy and scalable quantum machine learning.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•2 citations

Robustness Verification of Quantum Classifiers

Ji Guan, Wang Sheng Fang, Mingsheng Ying

Abstract Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be implemented on the near future quantum computers. However, quantum noise is a major obstacle to the practical implementation of quantum machine learning. In this work, we define a formal framework for the robustness verification and analysis of quantum machine learning algorithms against noises. A robust bound is derived and an algorithm is developed to check whether or not a quantum machine learning algorithm is robust with respect to quantum training data. In particular, this algorithm can find adversarial examples during checking. Our approach is implemented on Google’s TensorFlow Quantum and can verify the robustness of quantum machine learning algorithms with respect to a small disturbance of noises, derived from the surrounding environment. The effectiveness of our robust bound and algorithm is confirmed by the experimental results, including quantum bits classification as the “Hello World” example, quantum phase recognition and cluster excitation detection from real world intractable physical problems, and the classification of MNIST from the classical world.

arXiv:2008.07230•Lecture notes in computer science•Jan 1, 2021•38 citations

Adversarial robustness guarantees for quantum classifiers

Neil Dowling, Maxwell T. West, Angus Southwell +4 more

Abstract Despite their ever more widespread deployment throughout society, machine learning algorithms remain critically vulnerable to being spoofed by subtle adversarial tampering with their input data. The prospect of near-term quantum computers being capable of running quantum machine learning (QML) algorithms has therefore generated intense interest in their adversarial vulnerability. Here we show that quantum properties of QML algorithms can confer fundamental protections against such attacks, in certain scenarios guaranteeing robustness against classically-armed adversaries. We leverage tools from many-body physics to identify the quantum sources of this protection. Our results offer a theoretical underpinning of recent evidence which suggest quantum advantages in the search for adversarial robustness. In particular, we prove that quantum classifiers are: (i) protected against weak perturbations of data drawn from the trained distribution, (ii) protected against local attacks if they are insufficiently scrambling, and (iii) show evidence that they are protected against universal adversarial attacks if they are sufficiently chaotic. Our analytic results are supported by numerical evidence demonstrating the applicability of our theorems and the resulting robustness of a quantum classifier in practice. This line of inquiry constitutes a concrete pathway to advantage in QML, orthogonal to the usually sought improvements in model speed or accuracy.

arXiv:2405.10360•npj Quantum Information•Jan 19, 2026•10 citations

Quantum noise protects quantum classifiers against adversaries

Yuxuan Du, Min-Hsiu Hsieh, Tongliang Liu +2 more

Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies.However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy.It is then natural to ask: Can we harness the power of quantum noise that is beneficial to quantum computing?An important current direction for quantum computing is its application to machine learning, such as classification problems.One outstanding problem in machine learning for classification is its sensitivity to adversarial examples.These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers.They can also be considered as worst-case perturbations by unknown noise sources.We show that by taking advantage of depolarization noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise.This robustness property is intimately connected with an important security concept called differential privacy, which can be extended to quantum differential privacy.For the protection of quantum data, this quantum protocol can be used against the most general adversaries.Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of the classification model are absent, thus also providing a potential quantum advantage for classical data.This opens the opportunity to explore other ways in which quantum noise can be used in our favor, as well as identifying other ways quantum algorithms can be helpful in a way which is distinct from quantum speedups.

arXiv:2003.09416•Physical Review Research•May 27, 2021•157 citations

Enhancing adversarial robustness of quantum neural networks by adding noise layers

Chenyi Huang, Shibin Zhang

Abstract The rapid advancements in machine learning and quantum computing have given rise to a new research frontier: quantum machine learning. Quantum models designed for tackling classification problems possess the potential to deliver speed enhancements and superior predictive accuracy compared to their classical counterparts. However, recent research has revealed that quantum neural networks (QNNs), akin to their classical deep neural network-based classifier counterparts, are vulnerable to adversarial attacks. In these attacks, meticulously designed perturbations added to clean input data can result in QNNs producing incorrect predictions with high confidence. To mitigate this issue, we suggest enhancing the adversarial robustness of quantum machine learning systems by incorporating noise layers into QNNs. This is accomplished by solving a Min-Max optimization problem to control the magnitude of the noise, thereby increasing the QNN’s resilience against adversarial attacks. Extensive numerical experiments illustrate that our proposed method outperforms state-of-the-art defense techniques in terms of both clean and robust accuracy.

New Journal of Physics•Jul 19, 2023•13 citations
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.
Abstract Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.
Quantum Machine Learning (QML) fuses quantum computing with machine learning to address complex tasks with potential speedups over classical methods. While QML models such as variational quantum classifiers (QVC), quantum multilayer perceptron(QMLP) models and quantum convolutional neural networks (QCNN) have demonstrated promise in applications like image recognition and malware classification, they remain vulnerable to adversarial threats. Inspired by the vulnerabilities in classical ML, this work systematically investigates how attacks-ranging from training-time poisoning and inferencetime evasion (e.g., quantum versions of FGSM and PGD) to deployment-time trigger attacks-manifest in quantum circuits. We explore how classical adversarial strategies adapt to quantum models through parameterized encodings, hybrid architectures, and probabilistic outputs. The poster evaluates different quantum classifiers under adversarial settings, comparing their robustness, trainability, and resilience to perturbations. Defense mechanisms such as randomized encoding, engineered noise channels, and quantum adversarial training are analyzed in relation to specific threat types. In addition, we assess how quantum models behave differently than classical counterparts under attack, and how quantum-specific design constraints can either exacerbate or mitigate these effects. Our ultimate goal is to define and construct robust QML systems that are both theoretically sound and practically secure. By synthesizing results across multiple QML architectures and threat models, this work provides actionable insight into the development of resilient quantum classifiers, paving the way toward trustworthy and scalable quantum machine learning.
Abstract Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be implemented on the near future quantum computers. However, quantum noise is a major obstacle to the practical implementation of quantum machine learning. In this work, we define a formal framework for the robustness verification and analysis of quantum machine learning algorithms against noises. A robust bound is derived and an algorithm is developed to check whether or not a quantum machine learning algorithm is robust with respect to quantum training data. In particular, this algorithm can find adversarial examples during checking. Our approach is implemented on Google’s TensorFlow Quantum and can verify the robustness of quantum machine learning algorithms with respect to a small disturbance of noises, derived from the surrounding environment. The effectiveness of our robust bound and algorithm is confirmed by the experimental results, including quantum bits classification as the “Hello World” example, quantum phase recognition and cluster excitation detection from real world intractable physical problems, and the classification of MNIST from the classical world.
Abstract Despite their ever more widespread deployment throughout society, machine learning algorithms remain critically vulnerable to being spoofed by subtle adversarial tampering with their input data. The prospect of near-term quantum computers being capable of running quantum machine learning (QML) algorithms has therefore generated intense interest in their adversarial vulnerability. Here we show that quantum properties of QML algorithms can confer fundamental protections against such attacks, in certain scenarios guaranteeing robustness against classically-armed adversaries. We leverage tools from many-body physics to identify the quantum sources of this protection. Our results offer a theoretical underpinning of recent evidence which suggest quantum advantages in the search for adversarial robustness. In particular, we prove that quantum classifiers are: (i) protected against weak perturbations of data drawn from the trained distribution, (ii) protected against local attacks if they are insufficiently scrambling, and (iii) show evidence that they are protected against universal adversarial attacks if they are sufficiently chaotic. Our analytic results are supported by numerical evidence demonstrating the applicability of our theorems and the resulting robustness of a quantum classifier in practice. This line of inquiry constitutes a concrete pathway to advantage in QML, orthogonal to the usually sought improvements in model speed or accuracy.
Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies.However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy.It is then natural to ask: Can we harness the power of quantum noise that is beneficial to quantum computing?An important current direction for quantum computing is its application to machine learning, such as classification problems.One outstanding problem in machine learning for classification is its sensitivity to adversarial examples.These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers.They can also be considered as worst-case perturbations by unknown noise sources.We show that by taking advantage of depolarization noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise.This robustness property is intimately connected with an important security concept called differential privacy, which can be extended to quantum differential privacy.For the protection of quantum data, this quantum protocol can be used against the most general adversaries.Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of the classification model are absent, thus also providing a potential quantum advantage for classical data.This opens the opportunity to explore other ways in which quantum noise can be used in our favor, as well as identifying other ways quantum algorithms can be helpful in a way which is distinct from quantum speedups.
Abstract The rapid advancements in machine learning and quantum computing have given rise to a new research frontier: quantum machine learning. Quantum models designed for tackling classification problems possess the potential to deliver speed enhancements and superior predictive accuracy compared to their classical counterparts. However, recent research has revealed that quantum neural networks (QNNs), akin to their classical deep neural network-based classifier counterparts, are vulnerable to adversarial attacks. In these attacks, meticulously designed perturbations added to clean input data can result in QNNs producing incorrect predictions with high confidence. To mitigate this issue, we suggest enhancing the adversarial robustness of quantum machine learning systems by incorporating noise layers into QNNs. This is accomplished by solving a Min-Max optimization problem to control the magnitude of the noise, thereby increasing the QNN’s resilience against adversarial attacks. Extensive numerical experiments illustrate that our proposed method outperforms state-of-the-art defense techniques in terms of both clean and robust accuracy.