Quantum-inspired tensor networks algorithms have shown to be effective and efficient models for machine learning tasks, including anomaly detection. Here, we propose a highly parallelizable quantum-inspired approach which we call SMT-AD from Superposition of Multiresolution Tensors for Anomaly Detection. It is based upon the superposition of bond-dimension-1 matrix product operators to transform the input data with Fourier-assisted feature embedding, where the number of learnable parameters grows linearly with feature size, embedding resolutions, and the number of additional components in the matrix product operators structure. We demonstrate successful anomaly detection when applied to standard datasets, including credit card transactions, and find that, even with minimal configurations, it achieves competitive performance against established anomaly detection baselines. Furthermore, it provides a straightforward way to reduce the weight of the model and even improve the performance by highlighting the most relevant input features.
Quantum-inspired tensor networks algorithms have shown to be effective and efficient models for machine learning tasks, including anomaly detection. Here, we propose a highly parallelizable quantum-inspired approach which we call SMT-AD from Superposition of Multiresolution Tensors for Anomaly Detection. It is based upon the superposition of bond-dimension-1 matrix product operators to transform the input data with Fourier-assisted feature embedding, where the number of learnable parameters grows linearly with feature size, embedding resolutions, and the number of additional components in the matrix product operators structure. We demonstrate successful anomaly detection when applied to standard datasets, including credit card transactions, and find that, even with minimal configurations, it achieves competitive performance against established anomaly detection baselines. Furthermore, it provides a straightforward way to reduce the weight of the model and even improve the performance by highlighting the most relevant input features.
Quantum machine learning offers the ability to capture complex correlations in high-dimensional feature spaces, crucial for the challenge of detecting beyond the Standard Model physics in collider events, along with the potential for unprecedented computational efficiency in future quantum processors. Near-term utilization of these benefits can be achieved by developing quantum-inspired algorithms for deployment in classical hardware to enable applications at the "edge" of current scientific experiments. This work demonstrates the use of tensor networks for real-time anomaly detection in collider detectors. A spaced matrix product operator (SMPO) is developed that provides sensitivity to a variety beyond the Standard Model benchmarks, and can be implemented in field programmable gate array hardware with resources and latency consistent with trigger deployment. The cascaded SMPO architecture is introduced as an SMPO variation that affords greater flexibility and efficiency in ways that are key to edge applications in resource-constrained environments. These results reveal the benefit and near-term feasibility of deploying quantum-inspired ML in high energy colliders.
Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly detection with matrix product states on a discrete-valued cyber-security task, using quantum-inspired methods to gain insight into the learned model and detected anomalies. Here, we extend this framework to real-valued data domains. We furthermore introduce tree tensor networks for the task of explainable anomaly detection. We demonstrate these methods with three benchmark problems, show adequate predictive performance compared to several baseline models and both tensor network architectures' ability to explain anomalous samples. We thereby extend the application of tensor networks to a broader class of potential problems and open a pathway for future extensions to more complex tensor network architectures.
The emerging field of Quantum Machine Learning (QML) has shown promising advantages in accelerating processing speed and effectively handling the high dimensionality associated with complex datasets. Quantum Computing (QC) enables more efficient data manipulation through the quantum properties of superposition and entanglement. In this paper, we present a novel approach combining quantum and classical machine learning techniques to explore the impact of quantum properties for anomaly detection in Automatic Dependent Surveillance-Broadcast (ADS-B) data. We compare the performance of a Hybrid-Fully Connected Quantum Neural Network (H-FQNN) with different loss functions and use a publicly available ADSB dataset to evaluate the performance. The results demonstrate competitive performance in detecting anomalies, with accuracies ranging from 90.17% to 94.05%, comparable to the performance of a traditional Fully Connected Neural Network (FNN) model, which achieved accuracies between 91.50% and 93.37%.
Machine learning (ML) has achieved remarkable success in a wide range of applications. In recent ML research, deep anomaly detection (AD) has been a hot topic with the aim of discriminating among anomalous data with deep neural networks (DNNs). Notably, image AD is one of the most representative tasks in current deep AD research. ML's interaction with quantum computing is giving rise to a heated topic named quantum machine learning (QML), which enjoys great prospects according to recent academic research. This paper attempts to address the image AD problem in a deep manner with a novel QML solution. Specifically, we design a quantum-classical hybrid DNN (QHDNN) that aims to learn directly from normal raw images to train a normality model and then exclude images that do not conform to this model as anomalies during its inference. To enable the QHDNN to perform satisfactorily in deep image AD, we explore multiple quantum layer architectures and design a VQC-based QHDNN solution. Extensive experiments were conducted on commonly used benchmarks to test the proposed QML solution, whose results demonstrate the feasibility of addressing deep image AD with QML. Importantly, the experimental results show that our quantum-classical hybrid solution can even yield superior performance to that of its classical counterpart when they share the same number of learnable parameters.
This paper investigates the application of quantum-inspired principles to enhance anomaly detection using tensor decomposition. Traditional tensor decomposition methods, while effective, often struggle to fully capture the complex, non-linear relationships inherent in high-dimensional data, particularly when dealing with subtle anomalies. We propose a novel approach that leverages concepts from quantum mechanics, specifically tensor train (TT) representations with entanglement-like constraints, to improve anomaly detection performance. The core idea is that anomalies, by their very nature, represent deviations from the expected tensor structure. By incorporating constraints mimicking quantum entanglement, we aim to create tensor representations that are more sensitive to these deviations. We demonstrate, through theoretical analysis and conceptual development, the potential of this approach to improve anomaly detection accuracy. The methodology presented here offers a new perspective on tensor decomposition, moving beyond purely classical approaches and opening avenues for more robust and sensitive anomaly detection in diverse datasets. The focus is on the conceptual framework and the potential benefits rather than empirical validation due to the absence of experimental data.
Anomaly detection (AD) underpins fraud prevention, network security, industrial condition monitoring, medical diagnosis, and searches for new physics. However, it remains challenging due to rare anomalies, scarce labeled data, and the high dimensionality and strong correlation of sensor data. Many classical machine learning (ML) algorithms are designed to address AD in various settings, but the growth of quantum computing opens a new path for these problems. Quantum machine learning (QML) offers new tools, from exploring exponentially large Hilbert spaces and promising speed-ups to the native processing of quantum data. Thus, this review connects the two fields. We first present the basics of quantum computing, quantum algorithms, and QML with the most influential literature, and formalize the classical anomaly scores that quantum methods inherit. We then systematically review 30 primary studies of quantum anomaly detection (QAD) published between 2018 and 2026, express each method family through its anomaly score, and organize the field into a taxonomy of six families: quantum kernel methods, quantum autoencoders, quantum generative models, variational quantum classifiers, quantum linear-algebra methods, and detectors for quantum data. A cross-study analysis shows that the field has moved from asymptotic speed-up proposals to small hybrid experiments, that kernels and autoencoders dominate, that only nine studies run on gate-based hardware, and that none yet demonstrates a robust, practically relevant advantage over well-tuned classical detectors. We close with the main obstacles, such as data embedding, barren plateaus, kernel concentration, and weak baselines, and a research roadmap that prioritizes quantum data, fair benchmarks against classical baselines, and robust detectors for sequential and distributed data.