Qsco: A Quantum Scoring Module for Open-set Supervised Anomaly Detection

TL;DR

Open-set anomaly detection (OSAD) must identify unseen anomalies during training. The paper introduces Qsco, a Quantum Scoring Module that embeds a variational quantum circuit with $K$ qubits and depth $\ell$ into a neural backbone to learn high-dimensional anomaly distributions, encoding features as $\hat{\mathcal{X}}=\tanh(\mathcal{X}')$ and using Rot$(\cdot)=R_z(\lambda)R_y(\phi)R_x(\theta)$ gates with Ry rotations on inputs. The quantum circuit outputs $\hat{\mathcal{S}}$ which augments the backbone’s anomaly scoring, and experiments on eight real-world datasets show consistent AUC improvements with a practical ~20% per-epoch time overhead for $\tau=9$ qubits in Pennylane simulations. This work demonstrates a feasible, quantum-classical hybrid approach for OSAD in the NISQ era and motivates hardware-aware future integrations to further enhance anomaly detection capabilities.

Abstract

Open set anomaly detection (OSAD) is a crucial task that aims to identify abnormal patterns or behaviors in data sets, especially when the anomalies observed during training do not represent all possible classes of anomalies. The recent advances in quantum computing in handling complex data structures and improving machine learning models herald a paradigm shift in anomaly detection methodologies. This study proposes a Quantum Scoring Module (Qsco), embedding quantum variational circuits into neural networks to enhance the model's processing capabilities in handling uncertainty and unlabeled data. Extensive experiments conducted across eight real-world anomaly detection datasets demonstrate our model's superior performance in detecting anomalies across varied settings and reveal that integrating quantum simulators does not result in prohibitive time complexities. Our study validates the feasibility of quantum-enhanced anomaly detection methods in practical applications.

Figures (7)

• Figure 1: Visualization of the anomalies and normal data predicted by DRA ding2022catching and Qsco (Ours) in the MVTec AD Bergmann2019MVTecA dataset (carpet subset). The parameter $\ell$ controls the depth of the variational circuit in Qsco. With the correct $\ell$ level, Qsco enhances DRA's ability to distinguish boundaries between anomalies and normal data. However, if $\ell$ is too high ($\ell = 3$), it results in over-fitting, as shown in the last graph, while if $\ell$ is too low ($\ell = 1$), it leads to under-fitting.
• Figure 2: Overview of our proposed Qsco module. The left-hand section displays dataset samples from open set data, denoted as the input $\mathcal{X}$, which are fed into the feature extractor $\mathcal{F}\left ( \cdot \right )$ to obtain the feature map $\mathcal{X}'$. This feature map $\mathcal{X}'$ is the input to the quantum variational circuit. In the circuit, the $x$ values are used in the $RY(\cdot)$ gates, while the $\theta$ parameters are optimized during the training process in the $Rot(\cdot)$ operations. The green-shaded area represents the optimized layer in the Qsco module. The Qsco module output score is $\hat{\mathcal{S} }$.
• Figure 3: Visualization of the quantum state $\left | \rho \right \rangle$ on the Bloch sphere during the quantum downsampling process. The left, middle, and right figures depict the effects of the single-qubit rotation gates $RX$, $RY$, and $RZ$.
• Figure 4: Overview of our proposed Qsco module and classical DRA ding2022catching latent residual abnormality learning in a composite feature space.
• Figure 5: Performance Comparison of DRA and Qsco ($\bm{\ell = 2}$) with different numbers of anomaly examples. This comparison evaluates the performance (AUC score) of DRA and DRA + Qsco $\ell = 2$ under the same general settings across eight different datasets. The left side displays results for a single anomaly example, while the right shows results for ten. In the column chart, the ${\color{orange}\uparrow}$ indicates an improvement from the DRA model, and the ${\color{blue}\downarrow}$ signifies a decrease from the DRA.