Within the phenomenology of particle physics, the theoretical model of 4-zero textures is validated using a chi-square criterion that compares experimental data with the computational results of the model. Traditionally, analytical methods that often imply simplifications, combined with computational analysis, have been used to validate texture models. In this paper, we propose a new meta-heuristic variant of the differential evolution algorithm that incorporates aspects of the particle swarm optimization algorithm called “HE-DEPSO” to obtain chi-squared values that are less than a bound value, which exhaustive and traditional algorithms cannot obtain. The results show that the proposed algorithm can optimize the chi-square function according to the required criteria. We compare simulated data with experimental data in the allowed search region, thereby validating the 4-zero texture model.

Within the phenomenology of particle physics, the theoretical model of 4-zero textures is validated using a chi-square criterion that compares experimental data with the computational results of the model. Traditionally, analytical methods that often imply simplifications, combined with computational analysis, have been used to validate texture models. In this paper, we propose a new meta-heuristic variant of the differential evolution algorithm that incorporates aspects of the particle swarm optimization algorithm called "HE-DEPSO" to obtain chi-squared values are less than a bound value, which exhaustive and traditional algorithms cannot obtain. The results show that the proposed algorithm can optimize the chi-square function according to the required criteria. We compare simulated data with experimental data in the allowed search region, thereby validating the 4-zero texture model.

Clustering may uncover latent behavioral structure in Autism Spectrum Disorder (ASD) screening data without using outcome labels, but the resulting partitions depend strongly on data geometry and the adopted similarity measure. Quantum-hybrid clustering offers alternative distance and similarity estimators, yet whether these subroutines improve on classical methods under controlled conditions remains unclear. We conduct a benchmark of k-means, DBSCAN, agglomerative clustering, and spectral clustering against their quantum-hybrid counterparts. All methods are evaluated in a common 13-dimensional representation, with hyperparameters selected exclusively through internal validation indices. The evaluation covers four synthetic geometries and a 13-dimensional PCA representation of an ASD screening dataset, each containing 300 samples and evaluated over 10 seed-defined stochastic runs. Clustering quality is measured using the Silhouette Index (SI), Davies–Bouldin Index (DBI), Calinski–Harabasz Index (CHI), Adjusted Mutual Information (AMI), and Adjusted Rand Index (ARI). Under this validation protocol, Q-means exactly recovers the Gaussian clusters and improves label agreement on anisotropic data, but it does not outperform classical k-means on the ASD screening data. Q-spectral significantly reduces DBI on Two Moons, Concentric Rings, and ASD screening data, although these reductions do not consistently translate into higher AMI or ARI. Q-DBSCAN and Q-agglomerative exhibit greater sensitivity to distance distortions and finite-shot noise. Overall, the results reveal geometry-dependent trade-offs rather than uniform quantum-hybrid superiority. We relate these findings to theoretical complexity, measurement noise, state-preparation costs, and eigensolver bottlenecks in near-term implementations.

Quantum Machine Learning (QML) has been proposed as a framework that may offer theoretical advantages over classical machine learning, especially in computational complexity and parallel processing of high-dimensional data. However, due to the limitations imposed by the Noisy Intermediate-Scale Quantum (NISQ) era, implementing large-scale quantum algorithms remains infeasible, making hybrid quantum-classical approaches a more viable alternative. In this work, we formulate and implement custom quantum-hybrid versions of classical clustering algorithms and compare their performance on an Autism Spectrum Disorder (ASD) screening dataset, which represents a highly relevant clinical domain characterized by a complex mix of behavioral and demographic features. We evaluate classical k-means, DBSCAN, spectral clustering, and agglomerative clustering against these formulated quantum-hybrid implementations. For the evaluation, we use inner metrics (Silhouette, Davies-Bouldin, Calinski-Harabasz) and outer metrics (AMI, ARI) on the generated partitions. The results show that the formulated hybrid implementations achieve a partition quality comparable to that of classical counterparts, except in the case of Q-DBSCAN, where the classical algorithm outperformed our hybrid implementation due to the high-dimensional mapping. Thus, we present empirical information about strengths, weaknesses and potential viability of these formulated hybrid implementations in real-life applications in the NISQ era.