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International Joint Conference on Neural Networks (IJCNN)

Hybrid Quantum-Classical Framework for Anomaly Detection in Time Series with QUBO formulation and QAOA

Marco Casalbore, Leonardo Lavagna, Antonello Rosato, Massimo Panella

Published Jun 30, 2025• 2 citations
Publisher

Abstract

In this work, we introduce a hybrid quantum-classical framework to address anomaly detection problems in time series data using an innovative Quadratic Unconstrained Binary Optimization formulation. The proposed approach integrates density-based and statistical methodologies with the Quantum Approximate Optimization Algorithm, providing a versatile tool for anomaly detection. Moreover, the underlying model is transversal to different kinds of anomalies and can be directly applied to diverse applications, ranging from fault detection to novelty discovery. Experimental results prove that this architecture achieves competitive accuracy compared to classical techniques, with the unique advantage of exploring alternative solutions in parallel due to the properties of quantum computing. This capability enables a deeper understanding of patterns in time series data.

DOI
10.1109/ijcnn64981.2025.11228152

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In this work, we introduce a hybrid quantum-classical framework to address anomaly detection problems in time series data using an innovative Quadratic Unconstrained Binary Optimization formulation. The proposed approach integrates density-based and statistical methodologies with the Quantum Approximate Optimization Algorithm, providing a versatile tool for anomaly detection. Moreover, the underlying model is transversal to different kinds of anomalies and can be directly applied to diverse applications, ranging from fault detection to novelty discovery. Experimental results prove that this architecture achieves competitive accuracy compared to classical techniques, with the unique advantage of exploring alternative solutions in parallel due to the properties of quantum computing. This capability enables a deeper understanding of patterns in time series data.
We propose an enhanced hybrid quantum-classical framework for time series anomaly detection. Building on our previous formulation of the problem as a Quadratic Unconstrained Binary Optimization solved via the Quantum Approximate Optimization Algorithm, we extend the methodology with a statistical model selector and a refined set-covering inference scheme that accounts for temporal-value asymmetries. We analyze scalability in terms of qubit resources, assess feasibility on current quantum devices, and validate the approach on a benchmark of over one hundred heterogeneous time series. The results demonstrate interpretable decisions, robust precision, and competitive performance against both shallow classical local detectors and deep global classical architectures, highlighting the potential of the proposed methodology.
Anomaly detection is a crucial task in machine learning that involves identifying unusual patterns or events in data. It has numerous applications in various domains such as finance, healthcare, and cybersecurity. With the advent of quantum computing, there has been a growing interest in developing quantum approaches to anomaly detection. After reviewing traditional approaches to anomaly detection relying on statistical or distance-based methods, we will propose a Quadratic Unconstrained Binary Optimization (QUBO) model formulation of anomaly detection, compare it with classical methods, and discuss its scalability on current Quantum Processing Units (QPU).
Quantum Kernel Methods for Anomaly Detection in High-Velocity Data Streams introduces a novel framework leveraging quantum computing principles to address critical challenges in real-time anomaly detection. By combining the expressive power of quantum-enhanced feature spaces with classical machine learning techniques, the work presents a hybrid architecture capable of identifying subtle anomalies in complex, high-dimensional streaming data. The framework incorporates specialized quantum feature maps that efficiently encode temporal and distributional properties of data streams, while adaptation mechanisms respond to concept drift and evolving patterns. Through systematic experimental evaluation across synthetic and real-world datasets from financial transactions, network security, and industrial systems, the approach demonstrates superior detection performance particularly for complex nonlinear patterns in high-dimensional spaces. The quantum-classical implementation addresses current hardware constraints through optimization techniques and targeted resource allocation, establishing specific conditions where quantum advantage emerges for operational anomaly detection scenarios.
This study explores the integration of quantum computing techniques, specifically the Quantum Approximate Optimization Algorithm (QAOA), with classical portfolio optimization frameworks through the Quadratic Unconstrained Binary Optimization (QUBO) approach. Using monthly turnover data from the National Stock Exchange of India (NSE), this paper demonstrates the construction of a QUBO matrix by encoding expected returns and covariance-based risk profiles. Binary asset inclusion constraints are introduced into portfolios and then optimised using both brute force enumeration and quantum inspired solvers. The analysis reveals those combinations including Index Futures and Index Options exhibit superior risk-adjusted performance (Sharpe Ratio≈0.286\approx 0.286≈0.286). The hybrid approach suggests the promise of quantum inspired models as means to improve financial decision making under uncertainty. The results also give a robust template for scalable asset selection models that operate within the constraints of quantum computing infrastructure.
The integration of quantum algorithms into machine learning pipelines offers a promising direction for addressing complex combinatorial optimization problems inherent in graph-structured data. This study investigates the use of the Quantum Approximate Optimization Algorithm (QAOA) as a quantum subroutine within a hybrid quantum–classical framework to enhance machine learning solutions for graph-based tasks. QAOA is employed to solve NP-hard graph optimization problems such as Max-Cut, graph coloring, and community detection, which are reformulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. The solutions provided by QAOA are then incorporated into machine learning models, such as Graph Neural Networks (GNNs) or clustering algorithms, as enriched features or optimized graph partitions. The hybrid approach is evaluated on benchmark datasets, demonstrating competitive accuracy and improved scalability in certain problem instances compared to purely classical methods. The findings highlight the potential of leveraging near-term quantum hardware for augmenting classical learning systems in domains such as logistics, social network analysis, and computational biology.
Anomaly detection is an important problem with applications in various domains such as fraud detection, pattern recognition or medical diagnosis. Several algorithms have been introduced using classical computing approaches. However, using quantum computing for solving anomaly detection problems in time series data is a widely unexplored research field. This paper explores the application of quantum autoencoders to time series anomaly detection. We investigate two primary techniques for classifying anomalies: (1) Analyzing the reconstruction error generated by the quantum autoencoder and (2) latent representation analysis. Our simulated experimental results, conducted across various ansaetze, demonstrate that quantum autoencoders consistently outperform classical deep learning-based autoencoders across multiple datasets. Specifically, quantum autoencoders achieve superior anomaly detection performance while utilizing 60-230 times fewer parameters and requiring five times fewer training iterations. In addition, we implement our quantum encoder on real quantum hardware. Our experimental results demonstrate that quantum autoencoders achieve anomaly detection performance on par with their simulated counterparts.