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Qsco: A Quantum Scoring Module for Open-Set Supervised Anomaly Detection
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Proposes Qsco, a variational quantum circuit scoring module (PennyLane-simulated) plugged into the DRA open-set anomaly detector, evaluated on eight real-world AD datasets with noise-model robustness tests.
Problem
Open-set supervised anomaly detection: detecting both seen and unseen anomaly classes when only a few labeled anomalies are available during training.
Approach
Embeds a variational quantum circuit (RY/Rot rotations plus CNOT entanglement and Pauli-Z) as an additional scoring module inside a classical OSAD backbone (DRA), trained end-to-end with classical simulation in PennyLane.
Key results
- With one training anomaly, DRA+Qsco (l=2) improves AUC over DRA on most datasets, e.g. ELPV 0.626 to 0.749 and HeadCT 0.804 to 0.781 (decrease) with mixed results overall.
- Under ten training anomalies, DRA+Qsco does not consistently beat DRA; e.g. AITEX 0.886 (DRA) vs 0.875 (Qsco), while SDD improves 0.972 to 0.980.
- Qsco adds roughly 13-20% per-epoch time on the reported datasets; quantum simulation time grows from 13.11 s at 9 qubits to 182.19 s at 18 qubits.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add Qsco (ℓ = 2) to DRA | DRA · General setting, 10 training anomalies across eight datasets | AUC: AITEX: 0.886_{\pm 0.021} -> 0.875_{\pm 0.029}; SDD: 0.972_{\pm 0.010} -> 0.980_{\pm 0.007}; ELPV: 0.821_{\pm 0.028} -> 0 | Mixed |
| Add Qsco (ℓ = 2) to DRA | DRA · General setting, 1 training anomaly across eight datasets | AUC: AITEX: 0.703_{\pm 0.038} -> 0.708_{\pm 0.027}; SDD: 0.853_{\pm 0.056} -> 0.876_{\pm 0.032}; ELPV: 0.626_{\pm 0.074} -> 0 | Mixed |
| Increase Qsco circuit depth from ℓ = 2 to ℓ = 3 (ablation) | DRA + Qsco · General setting, 10 training anomalies across datasets | AUC | Mixed |
| Increase Qsco circuit depth from ℓ = 2 to ℓ = 3 (ablation) | DRA + Qsco · General setting, 1 training anomaly across datasets | AUC | Helped |
| Apply amplitude damping, phase-flip, depolarizing, or bit-flip noise to Qsco (ablation) | DRA + Qsco (ℓ = 2) · General setting, 10 training anomalies, seven datasets | AUC | Mixed |
| Apply quantum noise to Qsco (ablation) | DRA + Qsco (ℓ = 2) · General setting, 1 training anomaly, seven datasets | AUC | Mixed |
Surprising findings
- Adding Qsco to DRA does not consistently improve results in the ten-anomaly general setting, and some noise models sometimes improve performance on ELPV and Optical, which the authors attribute to regularization.
- Simulation time grows exponentially with qubit count, limiting scalability of classical simulation.
Limitations
- Classical simulation of the quantum circuit scales exponentially with qubit count, limiting scalability.
- Gains over DRA are inconsistent across datasets, especially with ten training anomalies.
- Results are simulated only, without execution on real quantum hardware.
Experimental setup
Datasets: MVTec AD AITEX SDD ELPV Optical BrainMRI HeadCT Hyper-Kvasir
Benchmarks: MVTec AD AITEX SDD ELPV Optical BrainMRI HeadCT Hyper-Kvasir
Metrics: AUC time per epoch (s)
Baselines: DRA DevNet SAOE FLOS MLEP
Builds on: DRA DevNet PennyLane
Closest papers by meaning
- Winning Lottery Tickets in Neural Networks via a Quantum-Inspired Classical Algorithm (NeurIPS 2026 · similarity 0.83)
- Limitations of measure-first protocols in quantum machine learning (ICML 2025 · similarity 0.83)
- TAPAS: Datasets for Learning the Learning with Errors Problem (NeurIPS 2025 · similarity 0.83)
- Training-Free Quantum Architecture Search (AAAI 2024 · similarity 0.83)
- On the Relation between Trainability and Dequantization of Variational Quantum Learning Models (ICLR 2025 · similarity 0.82)
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