Quantum anomaly detection in real scarce data

Emanuele Casciaro; Fabio Mascherpa; Alfonso Amendola; Filippo Caruso

quant-phOct 7, 2026

Quantum anomaly detection in real scarce data

Authors: Emanuele Casciaro, Fabio Mascherpa, Alfonso Amendola, Filippo Caruso

Organizations: Department of Physics and Astrophysics, University of Florence, Via Sansone, 1, Sesto Fiorentino, 50019, Italy · DICOX/C High Performance Computing Center of Excellence, DIT Digital & Information Technology, Eni S.p.A., Via Emilia 1, San Donato Milanese, 20097, Italy

Abstract

Anomaly detection on small and unbalanced datasets remains very challenging in machine learning, although this scenario is common in several domains, including healthcare, cybersecurity, finance, and energy. Data augmentation and generative AI may mitigate training-data scarcity, but they often fall short because anomalies are, by definition, unpredictable, rare, and highly diverse events compared to high-probability normal data. Overfitting to pseudo-anomalies, model collapse, high-dimensional data, uninterpretable black-box models, and validation challenges are typical issues limiting their practical applicability. In this context, quantum machine learning may provide a promising and more sustainable avenue because it can enable more interpretable models with far fewer trainable parameters and smaller datasets, implementable on energy-efficient quantum hardware. Here, we propose a novel two-step hybrid classical--quantum architecture for sequential data and test it on a realistic scenario in the global energy-transition domain, i.e., automated anomaly detection in large-scale photovoltaic plants. The achieved generalization capability and competitive prediction accuracy may pave the way for new hybrid learning models able to exploit the continuously increasing power of cloud-available and more sustainable quantum accelerators integrated with more traditional energy-hungry High Performance Computing resources.

Figures & tables

Figure 1: Current level of the first string of panels sampled over the course of the experiments. The peaks represent daytime activity, while the inactive regions are associated with nighttime.

Figure 2: Per-class feature distribution: due to the sane data being distributed all over the feature space, it is difficult to correctly identify the different types of fault instances.

Figure 3: Different hybrid interactions analyzed: no interactions (left) is compared against a hybrid model where the quantum layer is employed only at the classification level (ours, center), or from the beginning of the training (right). The black and red lines represent the flow of the input during the first and second training phase.

Figure 4: Anomaly detection over the last day of sampling. Both classic (left) and hybrid model (right) perform well, with the hybrid model avoiding some misclassification at the start of the sequence.

Figure 5: $Acc_{b}$ of each configuration of ansatz construction: without changing the measurement of the circuit (in our case $\braket{Z_{i}}$ ), the family of states $\ket{\psi(x;\theta)}$ associated with the circuit can have a great impact on the output of the layer, affecting the classification performances.

Figure 6: Circuit representation of the feature map encoding a sequence of $d=3$ dimensional data of length $T=4$ . Using different embedding strategies is possible to reduce the amount of qubits required for each element of the sequence, at the expense of a deeper circuit.

Figure 7: Ansatz used during the training: the data is encoded through the angle embedding $\ket{x}=\otimes_{i}R_{X}(x_{i})\ket{0}$ and processed using a variational layer.

Figure 8: Training scheme of the proposed architecture: once the autoencoder learns a suitable representation of the data, the decoder is replaced by the hybrid classifier.

Data incidence (%)
Sane	S. Circuit	Degradation	O. Circuit	Obscuration	All Anomalies
0.847	0.004	0.008	0.004	0.137	0.153

Table 1: Per-class distribution of each type of anomaly. The Sane state makes up for almost all the dataset size.

Model	$Acc$	$Acc_{b}$	$F1$	#Parameters
AE + QNN Classifier (ours)	0.9952	0.989	0.9955	82
Hybrid AE + Classical Classifier	0.7796	0.5	0.8617	18
AE + Classical Classifier	0.9956	0.9877	0.9959	$\approx 4400$ 1

Table 2: Experiment results for the binary prediction task. Our proposed model and its classical counterpart perform similarly well, while the HAE model fails to reliably detect anomalies.

Model	$Acc$	$Acc_{b}$	$F1$	#Parameters
AE + QNN Classifier (ours)	0.9357	0.9761	0.9418	109
Hybrid AE + Classical Classifier	0.8515	0.9293	0.8789	45
AE + Classical Classifier	0.8784	0.9549	0.9005	$\approx 4400$

Table 3: Classification scores in the AC task of the proposed models: while the HAE model has fewer parameters in the classifier with respect to our model, it shares a similar parametrized structure in the encoder.

Model	Sane	S. Circuit	Degradation	O. Circuit	Obscuration
AE + QNN Classifier (ours)	0.9481	0.9967	0.974	1	0.9653
AE + Classical Classifier	0.8881	0.9967	0.9846	1	0.9734

Table 4: Per-class accuracy score of the best performing models: our solution is less prone to flagging sane instances as anomalous data, resulting in a low false-positive count.

Encoding Layer
#	Strategy	Entanglement
1	$AE_{X}(x)$	No entanglement
2	$AE_{X}(x^{3})AE_{X}(x^{2})AE_{X}(x)$	No entanglement
3	Controlled $AE_{X}(x)$	Ring connectivity
4	Controlled $AE_{\vec{\sigma}}(x)$	Ring connectivity

Table 5: Encoding and variational strategies used in the construction of the ansatz; each encoding is tested in combination with every variational layer proposed.

AE_{a}(\cdot)

denotes the angle encoding with respect to the axis

a

, with

\vec{\sigma}

indicating a general Pauli axis.

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A core task in quantum anomaly detection is to compute an anomaly score that quantifies how strongly a test quantum state deviates from a given quantum dataset assumed to be normal. Classically, principal component analysis (PCA) for centered data computes the anomaly score by evaluating the test sample relative to the subspace spanned by the selected leading eigenvectors. However, for quantum data that lack a standard centering, explicitly recovering principal eigenvectors, constructing full Gram matrices, or loading quantum-random-access-memory-style data can be more costly than estimating the anomaly score itself. To avoid these costs, we propose Quantum Spectral Anomaly Detection (QSPADE), which computes PCA-like anomaly scores directly from the spectrum of the average state of the normal dataset. By replacing hard PCA rank selection with a smooth, temperature-controlled spectral threshold, QSPADE makes near-threshold spectral components contribute partially to the anomaly score. This makes the score vary continuously rather than jump when a borderline component is included or excluded, and makes it less sensitive to noise or arbitrary hard cutoffs near the threshold. In the zero-temperature limit, QSPADE recovers the hard-projector PCA score. The proposed measurement-based quantum detector can be calibrated with a sample complexity independent of the data dimension. Numerical simulations show that QSPADE behaves like kernel-PCA on encoded classical data and detects changes across a transverse-field Ising transition without predefined order parameters. Consequently, QSPADE gives an efficient framework for both quantum-kernel anomaly detection on encoded classical data and the monitoring of quantum-native systems where diagnostic observables are unknown.

Abstract

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