[C10] Semi-Supervised Multichannel Anomaly Detection Using QAOA-Driven Selection and Set Covering

In this paper we present a hybrid quantum–classical method for detecting anomalies in multivariate time series. We extend our previous approach to handle multiple correlated channels, which makes the problem more challenging because an anomaly can depend on the behavior of several variables at the same time. We formulate the selection of representative normal samples as a QUBO problem and use the Quantum Approximate Optimization Algorithm (QAOA) to solve it. The selected samples are then used as “anchors” for building local regions of normal behavior through a set-covering strategy and convex hulls. We use the available anomaly labels only during this second stage, mainly to stop the regions from including known anomalous samples. This allows us to keep the optimization itself mostly driven by the statistical structure and relationships within the data.

We test the method on both synthetic datasets and real water smart-meter data collected in Italy. The results show that our approach performs similarly to classical methods on the simpler synthetic data, while on the more challenging real-world dataset it achieves the best recall and F1-score among the methods we compare. In particular, the method is able to detect localized anomalies while still capturing the normal daily patterns in water consumption. Another interesting aspect is that QAOA can produce several equally good or nearly optimal solutions in a single run. These different solutions correspond to different sets of representative samples and therefore to different, but potentially valid, descriptions of normal behavior. Overall, we show that combining QAOA with a geometric set-covering approach can provide a competitive and interpretable way to detect anomalies in multivariate time series, although larger quantum resources may be needed to improve scalability in more complex settings. The article is available here. Code available here and related blog post here.