Q-matrices play a central role in cognitive diagnosis within educational data mining (EDM), specifying which latent skills each assessment item requires. Data-driven Q-matrix estimation remains challenging when assessments involve many correlated skills and when real response patterns depart from idealized generative assumptions. We introduce a novel quantum sparse autoencoder (QSAE) for Q-matrix estimation, which, to the best of our knowledge, is the first application of quantum machine learning (QML) to cognitive diagnosis. Overall, the QSAE embeds each student's binary response vector into a quantum circuit using an encoder, compresses it into a sparse latent representation, and maps that representation to the Q-matrix. We benchmark the QSAE against a classical autoencoder (CAE) across 60 simulated datasets and 9 real-world assessment datasets. The results reveal complementary strengths. Although the CAE partially achieves higher average accuracy under several simulation conditions, the QSAE is substantially more stable across replications, exhibiting lower variance in 49 of the 60 conditions. Moreover, on real assessment data, the QSAE outperforms the CAE on 6 of the 9 datasets. These findings suggest that the principal advancement of QML in this setting is not universal accuracy improvement, but enhanced robustness and capability to explore latent-structure complexity in real datasets.
Angle-encoded quantum kernels on tabular data collapse when the feature map is wider than the intrinsic dimension of the data. We propose the correlation fractal dimension D2 as an a priori qubit budget: encode D2 coordinates chosen by FD-ASE instead of the PCA-95% width or all E attributes. On nine data sets and a statevector simulator (n= 32), a one-layer ZZ fidelity kernel at q=D2 stays geometrically alive while the same kernel at the PCA-95% width has already collapsed. The budget is map-dependent: product-state and IQP maps overshoot it; a second ZZ layer undershoots it. Packed dense-angle and re-uploading encodings still live at the fractal q, but not when PCA-95% features are stacked onto those qubits. Shrinking the angle bandwidth moves the ZZ knee later; stretching it kills the kernel earlier. On IBM Quantum (ibm_fez, 256 shots, n=8) the one-layer ZZ kernel at the fractal width matches the exact kernel (MAE 0.021); past that width both hardware and simulator have collapsed. The ceiling is a property of the map-data pair at a stated bandwidth, not of the classical table alone.
Kernel methods are powerful tools in machine learning but commonly used full-Gram kernels face three key limitations: (1) quadratic scaling with training set size; (2) the use of fixed, non-trainable kernels; and (3) the absence of an intrinsic formulation for multiclass classification. We present McQuack, a trainable quantum kernel method for multiclass problems that achieves linear scaling in the number of training samples. This is accomplished by replacing the full training-set Gram matrix with a trainable sample-to-(class-centroid) fidelity matrix. We evaluate the model in simulation and on 124 qubits of two IBM devices, across more than 150 datasets. In simulation, McQuack outperforms existing "pure" quantum baselines, while results from hardware inference -- obtained without training -- achieve performance similar to an RBF kernel. Finally, we study the trainability of the model and observe no evidence of barren plateaus in our experiments with up to 13 qubits, and highlight the importance of parameter initialization for successful optimization.
Quantum federated learning enables distributed clients to train quantum neural networks without sharing local data, making it promising for privacy-aware intelligent services. Intelligent services in this context refer to privacy-sensitive distributed decision systems, such as fraud detection and genomic classification, where reliable and fair client-level learning is as important as the accuracy of the aggregate model. However, heterogeneous client data and noisy quantum optimization often cause unstable local updates, client drift, and unfair performance between clients. This paper proposes DUQFL-Prox, a drift-stable quantum federated learning framework based on deep-unfolded local optimization. Instead of using a fixed local optimizer, each client performs adaptive unfolded SPSA updates, while a proximal term keeps the local model close to the global model. A lightweight controller learns step-specific optimization parameters to improve post-aggregation performance. Experiments on financial fraud and genomic classification tasks show that DUQFL-Prox improves stability, generalization, and client fairness compared with standard QFL baselines. The results suggest that deep-unfolded quantum federated learning can support more reliable and fair intelligent services in heterogeneous distributed environments.
We characterize and compare the inherent interpretability offerings of a standard linear model with a single qubit mixed state model for the task of supervised binary classification. A side by side comparison reveals that a single qubit mixed state model for binary classification is just the ``ellipsoid version" of standard linear model classification. More precisely, rather than learning a hyperplane to classify data, we learn a hyperellipsoid. We discuss the consequences of the geometric inductive biases of both models, as well as how each model contains a different feature importance inductive bias. This short characterization offers an accessible route to quantum machine learning (ML) ideas for readers who have zero background in quantum and are only familiar with linear classification in ML. In support of ML pedagogy, we encourage instructors to utilize this piece to smoothly introduce quantum ML ideas into the undergraduate ML classroom.
Data scarcity and class imbalance are persistent challenges in machine learning that degrade model generalization and introduce predictive bias. We present a hybrid quantum-classical framework for synthetic data generation using a Quantum Circuit Born Machine (QCBM) to address these limitations. The proposed approach exploits quantum mechanical properties -- superposition and entanglement -- within a parameterized variational quantum circuit to model complex probability distributions that are difficult for classical generative methods to capture. Experiments are conducted on two tabular benchmark datasets: the Iris dataset and the Telco Customer Churn dataset. Preprocessing includes normalization and PCA-based dimensionality reduction to enable efficient basis encoding for quantum circuits. The QCBM is trained by minimizing Kullback-Leibler (KL) divergence between real and generated data distributions using a gradient-based parameter-shift optimization rule. Augmenting training data with QCBM-generated synthetic samples at 40-50% of the minority class improves F1-score by approximately 5-15% and minority-class recall by 10-25%. Cross-domain evaluations (Train on Synthetic, Test on Real; and Train on Real, Test on Synthetic) reveal a performance gap of only 3-10%, indicating strong distributional fidelity. Comparative analysis against classical oversampling methods -- SMOTE, Borderline-SMOTE, KMeansSMOTE, and SVM-SMOTE -- shows that QCBM achieves competitive classification performance and produces lower Maximum Mean Discrepancy (MMD) on the Telco dataset, suggesting superior structural similarity in certain imbalanced settings. These findings establish QCBM as a viable complementary tool for data augmentation, particularly for low-dimensional structured tabular data with class imbalance.
Diego Alvarez-Estevez, Alejandro Mayorga-Redondo, Eduardo Mosqueira-Reyquant-ph cs.LG
Dynamic Time Warping (DTW) is a cornerstone for time series classification, but its reliance on Euclidean distances fails to capture latent cross-channel correlations in complex multivariate data. We propose a hybrid Quantum Dynamic Time Warping (qDTW) architecture, replacing the classical distance metric with the parameterized geometry of a quantum Hilbert space. Through structural ablation on benchmarks up to $C=8$ spatial dimensions, we establish fundamental topological rules for quantum sequence alignment. We introduce a Unified Pre-Embedding Adjoint Ansatz that decouples trainable entanglement from classical data, eliminating the severe phase-scrambling and information bottlenecks inherent to traditional measurements. We demonstrate this decoupled architecture allows untrained quantum kernels to act as highly expressive baselines, while parameterized training effectively untangles deeply overlapping hyper-dimensional data. Furthermore, we identify a strict spatial-temporal expressivity tradeoff: temporal depth (data re-uploading) is necessary for dimensionally restricted univariate circuits, but applying it to wide multi-qubit registers triggers chaotic frequency-spectrum explosions and representation collapse. By navigating these topological hazards, our multivariate quantum architecture outperforms classical baselines, setting a new standard for integrating parameterized quantum circuits with dynamic programming