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.
We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register. From a Takens embedding and Vietoris--Rips filtration of S&P~500 returns, we extract combinatorial Laplacians and recast null-space counting as a continuous-PCE Rayleigh-quotient minimization with variational deflation, encoding $n_k$ simplex indices into $O(n_k^{1/\kappa})$ qubits with shallow, ancilla-free circuits. Because the resulting loss is rational rather than bilinear in the correlators, the barren-plateau bound of~\cite{Sciorilli25} does not transfer; empirically the gradient variance decays only polynomially, with no exponential barren plateau, over $n=4$--$12$ qubits. The classical stage matches ripser~\cite{bauer2021ripser} on all 190 sliding windows (2007-2009). On the real market Laplacians ($\beta_1=1$--$22$), warm-starting from a classical null-space surrogate allows PCE-VQE to recover $\beta_1$ exactly at every scale, placing the obstacle in the optimisation landscape rather than the encoding. Chronologically split classification gives in-regime ROC AUC $0.818$, but out-of-distribution evaluation on the 2020 COVID shock and 2022 rate cycle (AUC $0.009$, $0.515$) shows the calibration does not generalize across crisis regimes.
This paper investigates whether quantum principal component analysis can provide useful features for IDS without relying on claims of end-to-end quantum superiority, and finds that QPCA is most useful as a representation enhancer under NISQ-compatible, not hardware-validated, constraints.
Murilo Salem, D. Pontes, Luísa Böhm et al.· Anais do I Simpósio Brasilei...· 0 citations
This paper presents a comparative benchmarking study of classical and quantum machine learning models for intrusion detection using three benchmark datasets: NSL-KDD, UNSW-NB15, and MQTTEEB-D2025. The study evaluates how preprocessing choices, feature selection strategies, and quantum encoding methods influence model performance across datasets with different levels of noise and complexity. A unified pipeline is adopted, incorporating normalization, imbalance handling, dimensionality reduction, and two feature selection approaches: Random Forest importance and a quantum-aware method based on Quantum Kernel Alignment with Mutual Information. Four models are assessed: Support Vector Machine, Random Forest, Quantum Support Vector Machine, and Pegasos Quantum SVM. Results show that classical models remain stable across datasets, while quantum models are more sensitive to feature representation and kernel alignment. Quantum performance improves significantly with quantum-aware feature selection, particularly on cleaner datasets, whereas heterogeneous datasets remain challenging. Pegasos Quantum SVM offers a favorable balance between accuracy and computational efficiency, highlighting the importance of preprocessing alignment for practical quantum intrusion detection.
Taha M. Mahmoud, N. Kaabouch· 2026 6th International Confe...· 0 citations
We study the sample complexity of estimating and testing fundamental unitarily invariant properties of unknown quantum states; namely, the tasks of spectrum estimation, von Neumann entropy estimation, and rank-testing. For $d$-dimensional states, and for every $\gamma>0$, we prove a sample complexity lower bound of $\Omega(d^{2-\gamma})$ for spectrum estimation to constant sorted total-variation error, entropy estimation to constant additive error, and rank-testing to constant trace distance. Our hard instances are constructed from sandwiched products of Haar-random projectors, suitably normalized using a novel technique that lets us derive explicit expressions for high-order tensor moments of the resultant states. These moments can be expressed as symmetric functions of Jucys--Murphy elements of the symmetric group algebra. To show that two such mixtures are indistinguishable, we analyze the log-likelihood ratio and perform moment-matching, i.e., we set its low-order Jucys--Murphy components to zero. Indistinguishability is then obtained by bounding an $f$-divergence through the high-order components; the non-zero high-order terms and concentration of functions of Haar-random unitaries also imply separations in typical spectra, entropies, and ranks, proving all our lower bounds.
Marco Fanizza, R. O'Donnell, Chirag Wadhwa· 3 citations
Quantum kernel methods are a candidate approach for machine learning on near-term quantum hardware, but two practical problems limit their deployment: kernel values concentrate exponentially as the qubit count grows, and real-world datasets are often severely class-imbalanced. We present the first systematic empirical study of how these two effects interact. We define two diagnostic metrics, the Discrimination Ratio (DR) and the Quantum Imbalance Vulnerability Score (QIVS), which measure whether quantum kernels retain minority-class separability under concentration. Experiments span ten log-spaced imbalance ratios, five random seeds, five qubit counts (4 to 12), and five real-world datasets, and yield three results. First, DR stays above 1.0 at every qubit count tested (4 to 12), so the discriminative signal survives concentration. Second, at extreme imbalance (IR below 0.003), quantum kernel SVMs retain positive discriminative signal, crossing above DR=1.0 by IR≈0.0028, while the classical oversampling methods SMOTE and ADASYN produce zero minority-class recall throughout the same regime, a practical advantage for quantum kernels at the imbalance extreme. Third, QIVS follows a broadly monotonic decreasing trend, falling from 13.25 to 5.54 as the imbalance ratio increases, with a single minor fluctuation smaller than the cross-seed variability we measure elsewhere in the sweep. This trend makes QIVS a reliable diagnostic for practitioners choosing quantum kernels on imbalanced tasks.
Souvik Ghosh, Vijaysherly V.· 2026 International Conferenc...· 0 citations
Overall, quantum and hybrid autoencoders are not universally superior, but deliver competitive anomaly detection with remarkably high parametric efficiency.
Murilo Salem, D. Pontes, João Carrett et al.· Anais do I Simpósio Brasilei...· 0 citations