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arXiv:2212.02531 · Physical Review Research

Enhancing quantum adversarial robustness by randomized encodings

Weiyuan Gong, Yuan Dong, Weikang Li, Dong-Ling Deng

Published Apr 4, 2024• 40 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/physrevresearch.6.023020

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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 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.
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.
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 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 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.
State-of-the-art classical neural networks are observed to be vulnerable to small crafted adversarial perturbations. A more severe vulnerability has been noted for quantum machine learning (QML) models classifying Haar-random pure states. This stems from the concentration of measure phenomenon, a property of the metric space when sampled probabilistically, and is independent of the classification protocol. To provide insights into the adversarial robustness of a quantum classifier on real-world classification tasks, we focus on the adversarial robustness in classifying a subset of encoded states that are smoothly generated from a Gaussian latent space. We show that the vulnerability of this task is considerably weaker than that of classifying Haar-random pure states. In particular, we find only mildly polynomially decreasing robustness in the number of qubits, in contrast to the exponentially decreasing robustness when classifying Haar-random pure states and suggesting that QML models can be useful for real-world classification tasks.