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arXiv:2607.12055

HarmQ: Harmonic Backdoor Attacks Against Quantum Neural Networks

Junrui Zhang, Zemin Chen, Chunsheng Xin, Hongyi Wu, Rui Ning

quant-phSubmitted Jul 13, 2026• Announced Jul 15, 2026• 0 citations
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Abstract

Quantum Neural Networks (QNNs) have emerged as a promising paradigm for quantum machine learning in the Noisy Intermediate-Scale Quantum (NISQ) era, leveraging quantum phenomena such as superposition and entanglement to process information in exponentially large Hilbert spaces. However, QNNs inherit critical security vulnerabilities from classical neural networks, particularly susceptibility to backdoor attacks. Existing attack methods designed for classical systems fail against QNNs due to quantum-specific constraints: aggressive downsampling required by limited qubit resources destroys conventional triggers, while the spectral learning bias of parameterized quantum circuits (PQCs) restricts learnable patterns. To tackle this, we present HarmQ, a quantum-native backdoor attack that exploits PQCs' inherent Fourier decomposition bias through harmonic trigger patterns. Our approach employs sinusoidal perturbations on coarse grids with block-uniform structure, ensuring survival through downsampling while aligning with PQCs' preference for low-frequency components. This enables effective backdoor injection under realistic black-box conditions where attackers access only training data. Experiments on MNIST and Fashion-MNIST demonstrate that HarmQ achieves attack success rates exceeding 99% while maintaining over 90% clean accuracy, significantly outperforming existing methods including BadNets (2.77% ASR), Watermark (7.96% ASR), Q-FGSM (44.32% ASR) and QUAP (3.40% ASR). Parametric t-SNE visualizations of quantum state representations confirm that harmonic triggers create distinctly separated clusters, evidencing HarmQ as a fundamental security threat for QNNs.

Comments
8 pages, 6 figures. Accepted by the IEEE International Conference on Quantum Communications, Networking, and Computing (QCNC 2026)

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Quantum Neural Networks (QNNs) have emerged as a promising paradigm for quantum machine learning in the Noisy Intermediate-Scale Quantum (NISQ) era, leveraging quantum phenomena such as superposition and entanglement to process information in exponentially large Hilbert spaces. However, QNNs inherit critical security vulnerabilities from classical neural networks, particularly susceptibility to backdoor attacks. Existing attack methods designed for classical systems fail against QNNs due to quantum-specific constraints: aggressive downsampling required by limited qubit resources destroys conventional triggers, while the spectral learning bias of parameterized quantum circuits (PQCs) restricts learnable patterns. To tackle this, we present HarmQ, a quantum-native backdoor attack that exploits PQCs' inherent Fourier decomposition bias through harmonic trigger patterns. Our approach employs sinusoidal perturbations on coarse grids with block-uniform structure, ensuring survival through downsampling while aligning with PQCs' preference for low-frequency components. This enables effective backdoor injection under realistic black-box conditions where attackers access only training data. Experiments on MNIST and Fashion-MNIST demonstrate that HarmQ achieves attack success rates exceeding 99% while maintaining over 90% clean accuracy, significantly outperforming existing methods including BadNets (2.77% ASR), Watermark (7.96% ASR), Q-FGSM (44.32% ASR) and QUAP (3.40% ASR). Parametric t-SNE visualizations of quantum state representations confirm that harmonic triggers create distinctly separated clusters, evidencing HarmQ as a fundamental security threat for QNNs.
Quantum Neural Networks (QNNs) represent a promising paradigm for quantum machine learning in the Noisy Intermediate-Scale Quantum (NISQ) era, leveraging quantum phenomena such as superposition and entanglement to process information in exponentially large Hilbert spaces. However, QNNs inherit critical security vulnerabilities from classical neural networks, particularly susceptibility to backdoor attacks. Existing attack methods designed for classical systems fail against QNNs due to quantum-specific constraints: aggressive downsampling required by limited qubit resources destroys conventional triggers, while the spectral learning bias of parameterized quantum circuits (PQCs) restricts learnable patterns. To tackle this, we present HarmQ, a quantum-native backdoor attack that exploits PQCs' inherent Fourier decomposition bias through harmonic trigger patterns. Our approach employs sinusoidal perturbations on coarse grids with block-uniform structure, ensuring survival through downsampling while aligning with PQCs' preference for low-frequency components. This enables effective backdoor injection under realistic black-box conditions where attackers access only training data. Experiments on MNIST and Fashion-MNIST demonstrate that HarmQ achieves attack success rates exceeding 99% while maintaining over 90% clean accuracy, significantly outperforming existing methods including BadNets (2.77% ASR), Watermark (7.96% ASR), Q-FGSM (44.32% ASR) and QUAP (3.40% ASR). Parametric t-SNE visualizations of quantum state representations confirm that harmonic triggers create distinctly separated clusters, evidencing HarmQ as a fundamental security threat for QNNs.
Quantum Neural Networks (QNNs) are a promising framework for quantum machine learning on near-term quantum devices, but their security risks remain insufficiently understood. Studies have shown that QNNs are vulnerable to backdoor attacks, yet existing quantum backdoors mostly rely on a fixed trigger shared by all poisoned inputs. This fixed-trigger design is a major weakness because many defenses detect or weaken the repeated patterns such triggers leave in data representations. Although input-aware dynamic backdoors have been studied in classical neural networks, transferring them to QNNs is difficult because quantum learning introduces new obstacles. In particular, measurement compresses the post-ansatz quantum state into a limited classical output, weakening supervision for a trigger generator, while individual density matrices fluctuate with the input and make per-sample contrastive learning unstable. To address these challenges, we propose Q-DIBA, the first input-aware dynamic backdoor attack for QNNs. Q-DIBA jointly trains a classical trigger generator and a victim QNN through a three-mode mini-batch strategy that supports clean behavior, attack activation, and trigger specificity. To provide stable quantum-level supervision, Q-DIBA introduces an ensemble density contrastive loss that operates on post-ansatz quantum states before measurement and contrasts mode-averaged density matrices rather than individual samples. Experiments on MNIST and Fashion-MNIST across multiple QNN architectures show that Q-DIBA achieves high clean accuracy, strong attack success, and high cross-trigger accuracy, demonstrating effectiveness, stealthiness, and input specificity. The attack also remains resilient against defenses including visual inspection, spectral-signature detection, and fine-tuning, suggesting that input-aware quantum backdoors are an important threat to secure QNN deployment.
Quantum neural networks (QNNs) succeed in object recognition, natural language processing, and financial analysis. To maximize the accuracy of a QNN on a Noisy Intermediate Scale Quantum (NISQ) computer, approximate synthesis modifies the QNN circuit by reducing error-prone 2-qubit quantum gates. The success of QNNs motivates adversaries to attack QNNs via backdoors. However, naively transplanting backdoors designed for classical neural networks to QNNs yields only low attack success rate, due to the noises and approximate synthesis on NISQ computers. Prior quantum circuit-based backdoors cannot selectively attack some inputs or work with all types of encoding layers of a QNN circuit. Moreover, it is easy to detect both transplanted and circuit-based backdoors in a QNN. In this paper, we propose a novel and stealthy backdoor attack, QDoor, to achieve high attack success rate in approximately-synthesized QNN circuits by weaponizing unitary differences between uncompiled QNNs and their synthesized counterparts. QDoor trains a QNN behaving normally for all inputs with and without a trigger. However, after approximate synthesis, the QNN circuit always predicts any inputs with a trigger to a predefined class while still acts normally for benign inputs. Compared to prior backdoor attacks, QDoor improves the attack success rate by 13x and the clean data accuracy by 65% on average. Furthermore, prior backdoor detection techniques cannot find QDoor attacks in uncompiled QNN circuits.
Abstract Quantum neural networks (QNNs), as a novel model that combines the advantages of quantum computing and classical neural networks, are similarly vulnerable to backdoor attacks like classical neural networks. Current research on backdoor attacks against QNNs is limited by model structure or poisoning rate, resulting in poor attack performance in black-box scenarios. This paper proposes a black-box attack method that uses a quantum-classical hybrid generative model to generate transferable backdoor triggers for QNNs with unknown structures. The method generates universal adversarial perturbations as triggers based on generative models, and designs a QNN pool by utilizing the idea of ensemble models. It combines the min–max framework and non-target Kullback–Leibler divergence technique to improve the transferability of triggers to achieve a black-box attack. Experiments demonstrate that with a poisoning rate of only 5%, the attack success rate exceeds 98% for three different structured QNNs, proving the effectiveness of this backdoor attack. In addition, we also prove that the existing detection methods such as strip and spectral signatures are unable to defend against the backdoor attack proposed in this paper.
Quantum neural networks (QNNs), typically implemented via parameterized quantum circuits (PQCs), offer a potential route to quantum advantage in learning. We review recent progress through the Fourier structure of PQCs: the encoding Hamiltonian fixes the accessible frequency set, while training estimates the corresponding Fourier coefficients. This perspective explains how QNNs can mitigate the spectral bias that limits classical deep neural networks and motivates task-specialized designs. In particular, quantum ordinary differential equation (QODE) solver, quantum convolutional neural networks (QCNNs) and quantum reinforcement learning (QRL) exploit frequency pinching to better capture high-frequency image features and structured value landscapes. We further discuss trainability on noisy intermediate-scale quantum (NISQ) hardware, emphasizing Lie-algebraic and Fourier views of barren plateaus and practical mitigation strategies. Together, the Fourier and Lie perspectives yield concrete design principles and motivate quantum-native architectures built around spectral bias avoidance rather than classical imitation. Quantum neural networks (QNNs), implemented via parameterized quantum circuits (PQCs), promise a path to quantum advantage in learning by addressing the limitations of classical deep neural networks. Here, the authors explore the Fourier structure of PQCs to mitigate spectral bias, enhancing applications like quantum ODE solvers and quantum reinforcement learning, with implications for designing quantum-native architectures.
Backdoor attacks are emerging security threats to deep neural networks. In these attacks, adversaries manipulate the network by constructing training samples embedded with backdoor triggers. The backdoored model performs as expected on clean test samples but consistently misclassifies samples containing the backdoor trigger as a specific target label. While quantum neural networks (QNNs) have shown promise in surpassing their classical counterparts in certain machine learning tasks, they are also susceptible to backdoor attacks. However, current attacks on QNNs are constrained by the adversary’s understanding of the model structure and specific encoding methods. Given the diversity of encoding methods and model structures in QNNs, the effectiveness of such backdoor attacks remains uncertain. In this paper, we propose an algorithm that leverages dataset-based optimization to initiate backdoor attacks. A malicious adversary can embed backdoor triggers into a QNN model by poisoning only a small portion of the data. The victim QNN maintains high accuracy on clean test samples without the trigger but outputs the target label set by the adversary when predicting samples with the trigger. Furthermore, our proposed attack cannot be easily resisted by existing backdoor detection methods.