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arXiv:2102.07788 · National Science Review

Universal Adversarial Examples and Perturbations for Quantum Classifiers

Weiyuan Gong, Dong-Ling Deng

Published Jul 15, 2021• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1093/nsr/nwab130

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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.
Quantum artificial intelligence exploits the interplay between artificial intelligence and quantum physics: on the one hand, a plethora of tools and ideas from artificial intelligence can be adopted to tackle intricate quantum problems; on the other hand, quantum computing could also bring unprecedented opportunities to enhance, speed up, or innovate artificial intelligence. Yet, quantum learning systems, similar to classical ones, may also suffer adversarial attacks: 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 introduce the basic concepts and ideas of classical and quantum adversarial learning, as well as some recent advances along this line. First, we introduce the basics of both classical and quantum adversarial learning. Through concrete examples, involving classifications of phases of two-dimensional Ising model and three-dimensional chiral topological insulators, we reveal the vulnerability of classical machine learning phases of matter. In addition, we demonstrate the vulnerability of quantum classifiers with the example of classifying hand-written digit images. We theoretically elucidate the celebrated no free lunch theorem from the classical and quantum perspectives, and discuss the universality properties of adversarial attacks in quantum classifiers. Finally, we discuss the possible defense strategies. The study of adversarial learning in quantum artificial intelligence uncovers notable potential risks for quantum intelligence systems, which would have far-reaching consequences for the future interactions between the two areas.
Abstract Quantum adversarial machine learning is an emerging field that studies the vulnerability of quantum learning systems against adversarial perturbations and develops possible defense strategies. Quantum universal adversarial perturbations are small perturbations, which can make different input samples into adversarial examples that may deceive a given quantum classifier. This is a field that was rarely looked into but worthwhile investigating because universal perturbations might simplify malicious attacks to a large extent, causing unexpected devastation to quantum machine learning models. In this paper, we take a step forward and explore the quantum universal perturbations in the context of heterogeneous classification tasks. In particular, we find that quantum classifiers that achieve almost state-of-the-art accuracy on two different classification tasks can be both conclusively deceived by one carefully-crafted universal perturbation. This result is explicitly demonstrated with well-designed quantum continual learning models with elastic weight consolidation method to avoid catastrophic forgetting, as well as real-life heterogeneous datasets from hand-written digits and medical MRI images. Our results provide a simple and efficient way to generate universal perturbations on heterogeneous classification tasks and thus would provide valuable guidance for future quantum learning technologies.
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.
Quantum Machine Learning (QML) has emerged as a promising field of research, aiming to leverage the capabilities of quantum computing to enhance existing machine learning methodologies. Recent studies have revealed that, like their classical counterparts, QML models based on Parametrized Quantum Circuits (PQCs) are also vulnerable to adversarial attacks. Moreover, the existence of Universal Adversarial Perturbations (UAPs) in the quantum domain has been demonstrated theoretically in the context of quantum classifiers. In this work, we introduce QuGAP: a novel framework for generating UAPs for quantum classifiers. We conceptualize the notion of additive UAPs for PQC-based classifiers and theoretically demonstrate their existence. We then utilize generative models (QuGAP-A) to craft additive UAPs and experimentally show that quantum classifiers are susceptible to such attacks. Moreover, we formulate a new method for generating unitary UAPs (QuGAP-U) using quantum generative models and a novel loss function based on fidelity constraints. We evaluate the performance of the proposed framework and show that our method achieves state-of-the-art misclassification rates, while maintaining high fidelity between legitimate and adversarial samples.
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