Recently, quantum classifiers have been known to be vulnerable to adversarial attacks, where quantum classifiers are fooled by imperceptible noises to have misclassification. In this paper, we propose one first theoretical study that utilizing the added quantum random rotation noise can improve the robustness of quantum classifiers against adversarial attacks. We connect the definition of differential privacy and demonstrate the quantum classifier trained with the natural presence of additive noise is differentially private. Lastly, we derive a certified robustness bound to enable quantum classifiers to defend against adversarial examples supported by experimental results.
Recently, quantum classifiers have been known to be vulnerable to adversarial attacks, where quantum classifiers are fooled by imperceptible noises to have misclassification. In this paper, we propose one first theoretical study that utilizing the added quantum random rotation noise can improve the robustness of quantum classifiers against adversarial attacks. We connect the definition of differential privacy and demonstrate the quantum classifier trained with the natural presence of additive noise is differentially private. Lastly, we derive a certified robustness bound to enable quantum classifiers to defend against adversarial examples supported by experimental results.
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.
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.
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.
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/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, the increase in sample complexity due to adversarial training over conventional training vanishes in the limit of high dimensional inputs x. In contrast, when the adversary can directly attack the quantum state ρ(x) encoding the input 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.
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.