QARIMA: A Quantum Approach To Classical Time Series Analysis

We present a quantum-inspired ARIMA methodology that integrates quantum-assisted lag discovery with \emph{fixed-configuration} variational quantum circuits (VQCs) for parameter estimation and weak-lag refinement. Differencing and candidate lags are identified via swap-test-driven quantum autocorrelation (QACF) and quantum partial autocorrelation (QPACF), with a delayed-matrix construction that aligns quantum projections to time-domain regressors, followed by standard information-criterion parsimony. Given the screened orders $(p,d,q)$, we retain a fixed VQC ansatz, optimizer, and training budget, preventing hyperparameter leakage, and deploy the circuit in two estimation roles: VQC-AR for autoregressive coefficients and VQC-MA for moving-average coefficients. Between screening and estimation, a lightweight VQC weak-lag refinement re-weights or prunes screened AR lags without altering $(p,d,q)$. Across environmental and industrial datasets, we perform rolling-origin evaluations against automated classical ARIMA, reporting out-of-sample mean squared error (MSE), mean absolute percentage error (MAPE), and Diebold--Mariano tests on MSE and MAE. Empirically, the seven quantum contributions -- (1) differencing selection, (2) QACF, (3) QPACF, (4) swap-test primitives with delayed-matrix construction, (5) VQC-AR, (6) VQC weak-lag refinement, and (7) VQC-MA -- collectively reduce meta-optimization overhead and make explicit where quantum effects enter order discovery, lag refinement, and AR/MA parameter estimation.

Quantum-Inspired Geometric Classification with Correlation Group Structures and VQC Decision Modeling

We propose a geometry-driven quantum-inspired classification framework that integrates Correlation Group Structures (CGR), compact SWAP-test-based overlap estimation, and selective variational quantum decision modelling. Rather than directly approximating class posteriors, the method adopts a geometry-first paradigm in which samples are evaluated relative to class medoids using overlap-derived Euclidean-like and angular similarity channels. CGR organizes features into anchor-centered correlation neighbourhoods, generating nonlinear, correlation-weighted representations that enhance robustness in heterogeneous tabular spaces. These geometric signals are fused through a non-probabilistic margin-based fusion score, serving as a lightweight and data-efficient primary classifier for small-to-moderate datasets. On Heart Disease, Breast Cancer, and Wine Quality datasets, the fusion-score classifier achieves 0.8478, 0.8881, and 0.9556 test accuracy respectively, with macro-F1 scores of 0.8463, 0.8703, and 0.9522, demonstrating competitive and stable performance relative to classical baselines. For large-scale and highly imbalanced regimes, we construct compact Delta-distance contrastive features and train a variational quantum classifier (VQC) as a nonlinear refinement layer. On the Credit Card Fraud dataset (0.17% prevalence), the Delta + VQC pipeline achieves approximately 0.85 minority recall at an alert rate of approximately 1.31%, with ROC-AUC 0.9249 and PR-AUC 0.3251 under full-dataset evaluation. These results highlight the importance of operating-point-aware assessment in rare-event detection and demonstrate that the proposed hybrid geometric-variational framework provides interpretable, scalable, and regime-adaptive classification across heterogeneous data settings.

Quantum-Inspired Optimization Process for Data Imputation

Data imputation is a critical step in data pre-processing, particularly for datasets with missing or unreliable values. This study introduces a novel quantum-inspired imputation framework evaluated on the UCI Diabetes dataset, which contains biologically implausible missing values across several clinical features. The method integrates Principal Component Analysis (PCA) with quantum-assisted rotations, optimized through gradient-free classical optimizers -COBYLA, Simulated Annealing, and Differential Evolution to reconstruct missing values while preserving statistical fidelity. Reconstructed values are constrained within +/-2 standard deviations of original feature distributions, avoiding unrealistic clustering around central tendencies. This approach achieves a substantial and statistically significant improvement, including an average reduction of over 85% in Wasserstein distance and Kolmogorov-Smirnov test p-values between 0.18 and 0.22, compared to p-values > 0.99 in classical methods such as Mean, KNN, and MICE. The method also eliminates zero-value artifacts and enhances the realism and variability of imputed data. By combining quantum-inspired transformations with a scalable classical framework, this methodology provides a robust solution for imputation tasks in domains such as healthcare and AI pipelines, where data quality and integrity are crucial.

Quantum SMOTE with Angular Outliers: Redefining Minority Class Handling

This paper introduces Quantum-SMOTEV2, an advanced variant of the Quantum-SMOTE method, leveraging quantum computing to address class imbalance in machine learning datasets without K-Means clustering. Quantum-SMOTEV2 synthesizes data samples using swap tests and quantum rotation centered around a single data centroid, concentrating on the angular distribution of minority data points and the concept of angular outliers (AOL). Experimental results show significant enhancements in model performance metrics at moderate SMOTE levels (30-36%), which previously required up to 50% with the original method. Quantum-SMOTEV2 maintains essential features of its predecessor (arXiv:2402.17398), such as rotation angle, minority percentage, and splitting factor, allowing for tailored adaptation to specific dataset needs. The method is scalable, utilizing compact swap tests and low depth quantum circuits to accommodate a large number of features. Evaluation on the public Cell-to-Cell Telecom dataset with Random Forest (RF), K-Nearest Neighbours (KNN) Classifier, and Neural Network (NN) illustrates that integrating Angular Outliers modestly boosts classification metrics like accuracy, F1 Score, AUC-ROC, and AUC-PR across different proportions of synthetic data, highlighting the effectiveness of Quantum-SMOTEV2 in enhancing model performance for edge cases.

A Quantum Approach to Synthetic Minority Oversampling Technique (SMOTE)

The paper proposes the Quantum-SMOTE method, a novel solution that uses quantum computing techniques to solve the prevalent problem of class imbalance in machine learning datasets. Quantum-SMOTE, inspired by the Synthetic Minority Oversampling Technique (SMOTE), generates synthetic data points using quantum processes such as swap tests and quantum rotation. The process varies from the conventional SMOTE algorithm's usage of K-Nearest Neighbors (KNN) and Euclidean distances, enabling synthetic instances to be generated from minority class data points without relying on neighbor proximity. The algorithm asserts greater control over the synthetic data generation process by introducing hyperparameters such as rotation angle, minority percentage, and splitting factor, which allow for customization to specific dataset requirements. The approach is tested on a public dataset of TelecomChurn and evaluated alongside two prominent classification algorithms, Random Forest and Logistic Regression, to determine its impact along with varying proportions of synthetic data.