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

arXiv:2504.17690

On the Generalization of Adversarially Trained Quantum Classifiers

Petros Georgiou, Thomas, Aaron Mark, Sharu Theresa Jose, Osvaldo Simeone

Published Apr 24, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum classifiers are vulnerable to adversarial attacks that manipulate their input classical or quantum data. A promising countermeasure is adversarial training, where quantum classifiers are trained by using an attack-aware, adversarial loss function. This work establishes novel bounds on the generalization error of adversarially trained quantum classifiers when tested in the presence of perturbation-constrained adversaries. The bounds quantify the excess generalization error incurred to ensure robustness to adversarial attacks as scaling with the training sample size $m$ as $1/\sqrt{m}$, while yielding insights into the impact of the quantum embedding. For quantum binary classifiers employing \textit{rotation embedding}, we find that, in the presence of adversarial attacks on classical inputs $\mathbf{x}$, the increase in sample complexity due to adversarial training over conventional training vanishes in the limit of high dimensional inputs $\mathbf{x}$. In contrast, when the adversary can directly attack the quantum state $ρ(\mathbf{x})$ encoding the input $\mathbf{x}$, the excess generalization error depends on the choice of embedding only through its Hilbert space dimension. The results are also extended to multi-class classifiers. We validate our theoretical findings with numerical experiments.

DOI
10.48550/arxiv.2504.17690

Related papers

Adversarial Quantum Machine Learning: An Information-Theoretic Generalization Analysis

Petros Georgiou, Sharu Theresa Jose, Osvaldo Simeone

In a manner analogous to their classical counterparts, quantum classifiers are vulnerable to adversarial attacks that perturb their inputs. A promising countermeasure is to train the quantum classifier by adopting an attack-aware, or adversarial, loss function. This paper studies the generalization properties of quantum classifiers that are adversarially trained against bounded-norm white-box attacks. Specifically, a quantum adversary maximizes the classifier's loss by transforming an input state$\rho(x)$into a state$\tau$that is$\epsilon$-close to the original state$\rho(x)$in p-Schatten distance. Under suitable assumptions on the quantum embedding$\rho(x)$, we derive novel information-theoretic upper bounds on the generalization error of adversarially trained quantum classifiers for$p=1$and$p=\infty$. The derived upper bounds consist of two terms: the first is an exponential function of the 2-Renyi mutual information between classical data and quantum embedding, while the second term scales linearly with the adversarial perturbation size$\epsilon$. Both terms are shown to decrease as$1/\sqrt{T}$over the training set size$T$. An extension is also considered in which the adversary assumed during training has different parameters$p$and$\epsilon$as compared to the adversary affecting the test inputs. Finally, we validate our theoretical findings with numerical experiments for a synthetic setting.

arXiv:2402.00176•IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•6 citations

Enhancing quantum adversarial robustness by randomized encodings

Weiyuan Gong, Yuan Dong, Weikang Li +1 more

The interplay between quantum physics and machine learning gives rise to the emergent frontier of quantum machine learning, where advanced quantum learning models may outperform their classical counterparts in solving certain challenging problems. However, quantum learning systems are vulnerable to adversarial attacks: adding tiny carefully crafted perturbations on legitimate input samples can cause misclassifications. To address this problem, we propose an effective approach to protect quantum learning systems from adversarial attacks by randomly encoding the legitimate data samples through unitary or quantum error correction encoders that are unknown to the attackers. In particular, we rigorously prove that both global and local random unitary encoders lead to exponentially vanishing gradients (i.e., barren plateaus) for any variational quantum circuits that aim to add adversarial perturbations, independent of the input data and the inner structures of adversarial circuits and quantum classifiers. In addition, we prove a rigorous bound on the vulnerability of quantum classifiers under local unitary adversarial attacks. We show that random black-box quantum error correction encoders can protect quantum classifiers against local adversarial noises and their robustness increases as we concatenate error correction codes. To quantify the robustness enhancement, we adapt quantum differential privacy as a measure of the prediction stability for quantum classifiers. Our results establish versatile defense strategies for quantum classifiers against adversarial perturbations, which provide valuable guidance to enhance the reliability and security for both near-term and future quantum learning technologies. Published by the American Physical Society 2024

arXiv:2212.02531•Physical Review Research•Apr 4, 2024•40 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

Defending Quantum Classifiers against Adversarial Perturbations through Quantum Autoencoders

Emma Andrews, Sahan Sanjaya, Prabhat Mishra

Machine learning models can learn from data samples to carry out various tasks efficiently. When data samples are adversarially manipulated, such as by insertion of carefully crafted noise, it can cause the model to make mistakes. Quantum machine learning models are also vulnerable to such adversarial attacks, especially in image classification using variational quantum classifiers. While there are promising defenses against these adversarial perturbations, such as training with adversarial samples, they face practical limitations. For example, they are not applicable in scenarios where training with adversarial samples is either not possible or can overfit the models on one type of attack. In this paper, we propose an adversarial training-free defense framework that utilizes a quantum autoencoder to purify the adversarial samples through reconstruction. Moreover, our defense framework provides a confidence metric to identify potentially adversarial samples that cannot be purified the quantum autoencoder. Extensive evaluation demonstrates that our defense framework can significantly outperform state-of-the-art in prediction accuracy (up to 68%) under adversarial attacks.

quant-pharXiv:2604.28176•May 1, 2026•0 citations

Adversarial Attack Generation in Quantum Data Classification

Xiaokai Hou

Adversarial attack aims to generate infinitesimal perturbations that are crafted to deceive well-trained classifiers, and has been extensively explored in the context of classical data. However, the generation of adversarial attacks for quantum data remains largely unexplored. This work addresses this gap by investigating the efficacy of classical adversarial attack generation methods in the realm of quantum data learning. Specifically, we implement two widely recognized adversarial attack generation techniques, namely, the fast gradient sign method (FGSM) and the Deepfool method, for generating adversarial attacks on quantum data based on Gell-Mann matrices. We further evaluate the deceptive capabilities of these generated adversarial samples on a classical classifier tasked with entanglement discrimination. Through extensive numerical simulations, we demonstrate the effectiveness of our adversarial attack generation methods in efficiently crafting adversarial attacks on quantum data, successfully fooling the well-trained classifier. The outcomes of our research not only extend the applicability of classical machine learning algorithms to the domain of quantum machine learning but also provide valuable insights into the vulnerability of quantum data.

International Conference on Computer Science and Management Technology (ICCSMT)•Oct 13, 2023•1 citation

Universal Adversarial Examples and Perturbations for Quantum Classifiers

Weiyuan Gong, Dong-Ling Deng

Abstract Quantum machine learning explores the interplay between machine learning and quantum physics, which may lead to unprecedented perspectives for both fields. In fact, recent works have shown strong evidences that quantum computers could outperform classical computers in solving certain notable machine learning tasks. Yet, quantum learning systems may also suffer from the vulnerability problem: adding a tiny carefully-crafted perturbation to the legitimate input data would cause the systems to make incorrect predictions at a notably high confidence level. In this paper, we study the universality of adversarial examples and perturbations for quantum classifiers. Through concrete examples involving classifications of real-life images and quantum phases of matter, we show that there exist universal adversarial examples that can fool a set of different quantum classifiers. We prove that for a set of k classifiers with each receiving input data of n qubits, an $O(\frac{\ln k}{2^n})$ increase of the perturbation strength is enough to ensure a moderate universal adversarial risk. In addition, for a given quantum classifier we show that there exist universal adversarial perturbations, which can be added to different legitimate samples and make them to be adversarial examples for the classifier. Our results reveal the universality perspective of adversarial attacks for quantum machine learning systems, which would be crucial for practical applications of both near-term and future quantum technologies in solving machine learning problems.

arXiv:2102.07788•National Science Review•Jul 15, 2021•33 citations
Quantum classifiers are vulnerable to adversarial attacks that manipulate their input classical or quantum data. A promising countermeasure is adversarial training, where quantum classifiers are trained by using an attack-aware, adversarial loss function. This work establishes novel bounds on the generalization error of adversarially trained quantum classifiers when tested in the presence of perturbation-constrained adversaries. The bounds quantify the excess generalization error incurred to ensure robustness to adversarial attacks as scaling with the training sample size mmm as 1/m1/\sqrt{m}1/m​, while yielding insights into the impact of the quantum embedding. For quantum binary classifiers employing \textit{rotation embedding}, we find that, in the presence of adversarial attacks on classical inputs x\mathbf{x}x, the increase in sample complexity due to adversarial training over conventional training vanishes in the limit of high dimensional inputs x\mathbf{x}x. In contrast, when the adversary can directly attack the quantum state ρ(x)ρ(\mathbf{x})ρ(x) encoding the input x\mathbf{x}x, the excess generalization error depends on the choice of embedding only through its Hilbert space dimension. The results are also extended to multi-class classifiers. We validate our theoretical findings with numerical experiments.
In a manner analogous to their classical counterparts, quantum classifiers are vulnerable to adversarial attacks that perturb their inputs. A promising countermeasure is to train the quantum classifier by adopting an attack-aware, or adversarial, loss function. This paper studies the generalization properties of quantum classifiers that are adversarially trained against bounded-norm white-box attacks. Specifically, a quantum adversary maximizes the classifier's loss by transforming an input stateρ(x)\rho(x)ρ(x)into a stateτ\tauτthat isϵ\epsilonϵ-close to the original stateρ(x)\rho(x)ρ(x)in p-Schatten distance. Under suitable assumptions on the quantum embeddingρ(x)\rho(x)ρ(x), we derive novel information-theoretic upper bounds on the generalization error of adversarially trained quantum classifiers forp=1p=1p=1andp=∞p=\inftyp=∞. The derived upper bounds consist of two terms: the first is an exponential function of the 2-Renyi mutual information between classical data and quantum embedding, while the second term scales linearly with the adversarial perturbation sizeϵ\epsilonϵ. Both terms are shown to decrease as1/T1/\sqrt{T}1/T​over the training set sizeTTT. An extension is also considered in which the adversary assumed during training has different parameterspppandϵ\epsilonϵas compared to the adversary affecting the test inputs. Finally, we validate our theoretical findings with numerical experiments for a synthetic setting.
The interplay between quantum physics and machine learning gives rise to the emergent frontier of quantum machine learning, where advanced quantum learning models may outperform their classical counterparts in solving certain challenging problems. However, quantum learning systems are vulnerable to adversarial attacks: adding tiny carefully crafted perturbations on legitimate input samples can cause misclassifications. To address this problem, we propose an effective approach to protect quantum learning systems from adversarial attacks by randomly encoding the legitimate data samples through unitary or quantum error correction encoders that are unknown to the attackers. In particular, we rigorously prove that both global and local random unitary encoders lead to exponentially vanishing gradients (i.e., barren plateaus) for any variational quantum circuits that aim to add adversarial perturbations, independent of the input data and the inner structures of adversarial circuits and quantum classifiers. In addition, we prove a rigorous bound on the vulnerability of quantum classifiers under local unitary adversarial attacks. We show that random black-box quantum error correction encoders can protect quantum classifiers against local adversarial noises and their robustness increases as we concatenate error correction codes. To quantify the robustness enhancement, we adapt quantum differential privacy as a measure of the prediction stability for quantum classifiers. Our results establish versatile defense strategies for quantum classifiers against adversarial perturbations, which provide valuable guidance to enhance the reliability and security for both near-term and future quantum learning technologies. Published by the American Physical Society 2024
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.
Machine learning models can learn from data samples to carry out various tasks efficiently. When data samples are adversarially manipulated, such as by insertion of carefully crafted noise, it can cause the model to make mistakes. Quantum machine learning models are also vulnerable to such adversarial attacks, especially in image classification using variational quantum classifiers. While there are promising defenses against these adversarial perturbations, such as training with adversarial samples, they face practical limitations. For example, they are not applicable in scenarios where training with adversarial samples is either not possible or can overfit the models on one type of attack. In this paper, we propose an adversarial training-free defense framework that utilizes a quantum autoencoder to purify the adversarial samples through reconstruction. Moreover, our defense framework provides a confidence metric to identify potentially adversarial samples that cannot be purified the quantum autoencoder. Extensive evaluation demonstrates that our defense framework can significantly outperform state-of-the-art in prediction accuracy (up to 68%) under adversarial attacks.
Adversarial attack aims to generate infinitesimal perturbations that are crafted to deceive well-trained classifiers, and has been extensively explored in the context of classical data. However, the generation of adversarial attacks for quantum data remains largely unexplored. This work addresses this gap by investigating the efficacy of classical adversarial attack generation methods in the realm of quantum data learning. Specifically, we implement two widely recognized adversarial attack generation techniques, namely, the fast gradient sign method (FGSM) and the Deepfool method, for generating adversarial attacks on quantum data based on Gell-Mann matrices. We further evaluate the deceptive capabilities of these generated adversarial samples on a classical classifier tasked with entanglement discrimination. Through extensive numerical simulations, we demonstrate the effectiveness of our adversarial attack generation methods in efficiently crafting adversarial attacks on quantum data, successfully fooling the well-trained classifier. The outcomes of our research not only extend the applicability of classical machine learning algorithms to the domain of quantum machine learning but also provide valuable insights into the vulnerability of quantum data.
Abstract Quantum machine learning explores the interplay between machine learning and quantum physics, which may lead to unprecedented perspectives for both fields. In fact, recent works have shown strong evidences that quantum computers could outperform classical computers in solving certain notable machine learning tasks. Yet, quantum learning systems may also suffer from the vulnerability problem: adding a tiny carefully-crafted perturbation to the legitimate input data would cause the systems to make incorrect predictions at a notably high confidence level. In this paper, we study the universality of adversarial examples and perturbations for quantum classifiers. Through concrete examples involving classifications of real-life images and quantum phases of matter, we show that there exist universal adversarial examples that can fool a set of different quantum classifiers. We prove that for a set of k classifiers with each receiving input data of n qubits, an O(ln⁡k2n)O(\frac{\ln k}{2^n})O(2nlnk​) increase of the perturbation strength is enough to ensure a moderate universal adversarial risk. In addition, for a given quantum classifier we show that there exist universal adversarial perturbations, which can be added to different legitimate samples and make them to be adversarial examples for the classifier. Our results reveal the universality perspective of adversarial attacks for quantum machine learning systems, which would be crucial for practical applications of both near-term and future quantum technologies in solving machine learning problems.