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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Anomaly Detection Based on Quantum Autoencoder

Siqi Li, Zikun Zhang, Xun Zhu, Yanni Ou, Kun Xu

Published Jun 23, 2025• 0 citations
Publisher

Abstract

Quantum autoencoder (QAE) is a key tool in quantum machine learning and can be applied to areas such as dimensionality reduction and feature extraction [1]. Anomaly detection identifies deviations from normal patterns, which is crucial yet challenging due to the need to detect risks while minimizing false positives [2]. We propose a QAE-based anomaly detection scheme using an optical quantum neural network. Figure 1 (A) shows the basic structure of the QAE: the encoder compresses the input quantum state into a low-dimensional latent space, and the decoder reconstructs the original quantum state from the latent space. QAE-based anomaly detection works by learning the low-dimensional features of normal data and minimizing its reconstruction error. Normal data can be well reconstructed, while anomalous data exhibits a larger reconstruction error. When the reconstruction error of test data exceeds a set threshold, it is classified as anomalous. We constructed the QAE using an optical quantum neural network consisting of 50:50 beam splitters and controllable phase shifters [3]. Due to the unitary matrix property, only the encoder needs to be trained, and the decoder is simply the conjugate transpose of the encoder. To compress an N-dimensional quantum state$\rho$into${K}$dimensions, efficient compression can be achieved by minimizing the expectation value of the projection onto the trash state, given by$C(\theta,\phi)=Tr\left(PU(\theta,\phi)\rho U^+(\theta,\phi)\right)$[4]. Here,$P=(I_{K}\oplus\vert 0\rangle^{\otimes N-K}\langle 0\vert ^{\otimes(N-K)})$represents the projection onto the trash state,$I_{K}$is the K-dimensional identity matrix,$\vert 0\rangle^{\otimes(N-K)}\text{is}$the trash state,$Tr$denotes the trace,$U(\theta,\phi)$is the encoder with adjustable parameters, and$U\dagger(\theta_,\phi)$is the decoder. We only need to train the encoder during the training process, and the decoder is simply its conjugate transpose.

DOI
10.1109/cleo/europe-eqec65582.2025.11110982

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Quantum autoencoder (QAE) is a key tool in quantum machine learning and can be applied to areas such as dimensionality reduction and feature extraction [1]. Anomaly detection identifies deviations from normal patterns, which is crucial yet challenging due to the need to detect risks while minimizing false positives [2]. We propose a QAE-based anomaly detection scheme using an optical quantum neural network. Figure 1 (A) shows the basic structure of the QAE: the encoder compresses the input quantum state into a low-dimensional latent space, and the decoder reconstructs the original quantum state from the latent space. QAE-based anomaly detection works by learning the low-dimensional features of normal data and minimizing its reconstruction error. Normal data can be well reconstructed, while anomalous data exhibits a larger reconstruction error. When the reconstruction error of test data exceeds a set threshold, it is classified as anomalous. We constructed the QAE using an optical quantum neural network consisting of 50:50 beam splitters and controllable phase shifters [3]. Due to the unitary matrix property, only the encoder needs to be trained, and the decoder is simply the conjugate transpose of the encoder. To compress an N-dimensional quantum stateρ\rhoρintoK{K}Kdimensions, efficient compression can be achieved by minimizing the expectation value of the projection onto the trash state, given byC(θ,ϕ)=Tr(PU(θ,ϕ)ρU+(θ,ϕ))C(\theta,\phi)=Tr\left(PU(\theta,\phi)\rho U^+(\theta,\phi)\right)C(θ,ϕ)=Tr(PU(θ,ϕ)ρU+(θ,ϕ))[4]. Here,P=(IK⊕∣0⟩⊗N−K⟨0∣⊗(N−K))P=(I_{K}\oplus\vert 0\rangle^{\otimes N-K}\langle 0\vert ^{\otimes(N-K)})P=(IK​⊕∣0⟩⊗N−K⟨0∣⊗(N−K))represents the projection onto the trash state,IKI_{K}IK​is the K-dimensional identity matrix,∣0⟩⊗(N−K)is\vert 0\rangle^{\otimes(N-K)}\text{is}∣0⟩⊗(N−K)isthe trash state,TrTrTrdenotes the trace,U(θ,ϕ)U(\theta,\phi)U(θ,ϕ)is the encoder with adjustable parameters, andU†(θ,ϕ)U\dagger(\theta_,\phi)U†(θ,​ϕ)is the decoder. We only need to train the encoder during the training process, and the decoder is simply its conjugate transpose.
Quantum convolutional neural networks (QCNNs) have become increasingly popular in quantum machine learning (QML) due to their efficient parameterization and hierarchical representation of quantum information. Anomaly detection is an important machine learning task with applications across a wide range of domains, including scientific data analysis. In this work, we adapt a QCNN architecture into a quantum autoencoder (QAE) framework for reconstruction-based anomaly detection. The models are trained in a semi-supervised manner on normal samples to reconstruct feature-extracted and dimensionally reduced time-series data, with reconstruction error used as an anomaly score. We investigate two quantum convolutional autoencoder architectures that differ in their treatment of latent information: a hierarchical architecture in which information remains distributed across the circuit and a bottleneck-based architecture in which information is explicitly compressed and reconstructed using additional decoder qubits. The size of the quantum latent space is varied to study its influence on reconstruction accuracy and anomaly detection performance. The approaches are benchmarked against both a variational quantum circuit and a comparable classical baseline using a real-world exoplanet anomaly-detection dataset. Results indicate a trade-off between latent-space size and model capacity, while also suggesting that explicit latent-space compression through a quantum bottleneck can improve anomaly detection performance relative to architectures that retain information throughout the circuit.
The practical value of quantum machine learning for network anomaly detection remains unclear under controlled and comparable benchmarking conditions. This study evaluates a trash-qubit-based Quantum Autoencoder (QAE) against seven classical anomaly-detection methods on UNSW-NB15 using shared data partitions, preprocessing steps, model selection procedures, and threshold calibration protocols. The experimental design included five independent seeds, three training set sizes, two feature budgets, and 12 QAE architectures, together with low-FPR analysis, finite-shot and synthetic-noise evaluation, less-constrained classical reference settings, and a cross-dataset assessment on TON_IoT. The Angle-RY encoding with a Real-Amplitudes Ring ansatz at depth L = 2 achieved the highest mean validation-selection AUPRC. On UNSW-NB15, the QAE was competitive in AUPRC and AUROC but remained behind the strongest classical baselines in F1-score, and its attack recall declined sharply under low-FPR constraints. The TON_IoT results further showed that relative model performance depended on the dataset. Under finite-shot and synthetic-noise conditions, anomaly-score rankings were largely preserved, whereas threshold-based decisions were more sensitive. Overall, the QAE showed competitive continuous-score discrimination on UNSW-NB15, but achieving reliable detection at low false-alarm rates remains a key operational challenge.
Abstract Anomaly detection in cybersecurity is a challenging task, where normal events far outnumber anomalous ones with new anomalies occurring frequently. Classical autoencoders have been used for anomaly detection, but struggles in data-limited settings which quantum counterparts can potentially overcome. In this work, we apply Quantum Autoencoders (QAEs) for anomaly detection in cybersecurity, specifically on the BPF-extended tracking honeypot (BETH) dataset. QAEs are evaluated across multiple encoding techniques, ansatz types, repetitions, and feature selection strategies. Our results demonstrate that an 8-feature QAE using Dense-Angle encoding with a RealAmplitude ansatz can outperform Classical Autoencoders (CAEs), even when trained on substantially fewer samples. The effects of quantum encoding and feature selection for developing quantum models are demonstrated and discussed. In a data-limited setting, the best performing QAE model has a F1 score of 0.87, better than that of CAE (0.77). These findings suggest that QAEs may offer practical advantages for anomaly detection in data-limited scenarios.
We study a quantum autoencoder (QAE) for compression-driven anomaly detection in brain MRI data. The approach leverages angle encoding to map image patches into quantum states, followed by a variational encoder-decoder architecture trained to discard information via auxiliary trash qubits. Anomaly scores reflect the degree to which inputs resist compression relative to normal data, with higher scores corresponding to deviations from the learned normal manifold. Evaluated on publicly available brain MRI DICOM datasets, the method achieves a slice-level ROC-AUC of approximately 0.95 and a patch-level ROC-AUC of approximately 0.813, outperforming classical autoencoder and PCA baselines. Analysis of the learned parameters reveals a pronounced encoder-decoder asymmetry, where effective anomaly detection arises from structured information compression within the encoder rather than increased parameter magnitude or decoder expressivity. This results in a controlled compression-reconstruction trade-off with a clear operating regime that supports principled threshold selection. Qualitative evaluation further shows that the QAE produces spatially localized anomaly heatmaps aligned with tumorous regions. The results, supported by promising baseline performances, demonstrate that quantum autoencoders provide an interpretable and controllable mechanism for anomaly detection based on incompressibility with respect to a learned latent representation. This work highlights the potential of quantum autoencoders as a principled tool for studying compression dynamics in quantum machine learning, with promising implications for decision support in medical imaging workflows.
Anomaly Detection (AD) defines the task of identifying observations or events that deviate from typical - or normal - patterns, a critical capability in IT security for recognizing incidents such as system misconfigurations, malware infections, or cyberattacks. In enterprise environments like SAP HANA Cloud systems, this task often involves monitoring high-dimensional, multivariate time series (MTS) derived from telemetry and log data. With the advent of quantum machine learning offering efficient calculations in high-dimensional latent spaces, many avenues open for dealing with such complex data. One approach is the Quantum Autoencoder (QAE), an emerging and promising method with potential for application in both data compression and AD. However, prior applications of QAEs to time series AD have been restricted to univariate data, limiting their relevance for real-world enterprise systems. In this work, we introduce a novel QAE-based framework designed specifically for MTS AD towards enterprise scale. We theoretically develop and experimentally validate the architecture, demonstrating that our QAE achieves performance competitive with neural-network-based autoencoders while requiring fewer trainable parameters. We evaluate our model on datasets that closely reflect SAP system telemetry and show that the proposed QAE is a viable and efficient alternative for semisupervised AD in real-world enterprise settings.
The integration of Quantum Computing and Machine Learning (QML) holds transformative potential for intelligent data analysis, especially in processing high-dimensional and complex datasets. This paper proposes a hybrid quantum-classical framework for proactive anomaly detection, combining Quantum Auto-Encoders (QAEs) for feature compression with Quantum k-Nearest Neighbors (QkNN) for classification. Tailored for high-stakes domains like cybersecurity and IoT analytics, the approach leverages quantum entanglement and exponential state-space properties to enhance anomaly identification accuracy and efficiency. QAEs capture latent representations of typical behavior, while QkNN applies quantum parallelism to classify deviations against known patterns. Evaluations on standard benchmark datasets demonstrate the proposed QAE+QkNN framework’s superiority in precision, scalability, and resilience, particularly under noisy and sparse data conditions. While current limitations in quantum hardware pose constraints, the results underscore the method’s practical viability and promise. This study contributes to the growing body of QML research and highlights the potential of quantum-augmented detection systems in enabling the next generation of real-time, intelligent monitoring solutions.