Non-Convex Portfolio Optimization via Energy-Based Models: A Comparative Analysis Using the Thermodynamic HypergRaphical Model Library (THRML) for Index Tracking

Portfolio optimization under cardinality constraints transforms the classical Markowitz mean-variance problem from a convex quadratic problem into an NP-hard combinatorial optimization problem. This paper introduces a novel approach using THRML (Thermodynamic HypergRaphical Model Library), a JAX-based library for building and sampling probabilistic graphical models that reformulates index tracking as probabilistic inference on an Ising Hamiltonian. Unlike traditional methods that seek a single optimal solution, THRML samples from the Boltzmann distribution of high-quality portfolios using GPU-accelerated block Gibbs sampling, providing natural regularization against overfitting. We implement three key innovations: (1) dynamic coupling strength that scales inversely with market volatility (VIX), adapting diversification pressure to market regimes; (2) rebalanced bias weights prioritizing tracking quality over momentum for index replication; and (3) sector-aware post-processing ensuring institutional-grade diversification. Backtesting on a 100-stock S and P 500 universe from 2023 to 2025 demonstrates that THRML achieves 4.31 percent annualized tracking error versus 5.66 to 6.30 percent for baselines, while simultaneously generating 128.63 percent total return against the index total return of 79.61 percent. The Diebold-Mariano test confirms statistical significance with p less than 0.0001 across all comparisons. These results position energy-based models as a promising paradigm for portfolio construction, bridging statistical mechanics and quantitative finance.

Q2SAR: A Quantum Multiple Kernel Learning Approach for Drug Discovery

Quantitative Structure-Activity Relationship (QSAR) modeling is a cornerstone of computational drug discovery. This research demonstrates the successful application of a Quantum Multiple Kernel Learning (QMKL) framework to enhance QSAR classification, showing a notable performance improvement over classical methods. We apply this methodology to a dataset for identifying DYRK1A kinase inhibitors. The workflow involves converting SMILES representations into numerical molecular descriptors, reducing dimensionality via Principal Component Analysis (PCA), and employing a Support Vector Machine (SVM) trained on an optimized combination of multiple quantum and classical kernels. By benchmarking the QMKL-SVM against a classical Gradient Boosting model, we show that the quantum-enhanced approach achieves a superior AUC score, highlighting its potential to provide a quantum advantage in challenging cheminformatics classification tasks.

A Laplacian-based Quantum Graph Neural Network for Semi-Supervised Learning

Laplacian learning method is a well-established technique in classical graph-based semi-supervised learning, but its potential in the quantum domain remains largely unexplored. This study investigates the performance of the Laplacian-based Quantum Semi-Supervised Learning (QSSL) method across four benchmark datasets -- Iris, Wine, Breast Cancer Wisconsin, and Heart Disease. Further analysis explores the impact of increasing Qubit counts, revealing that adding more Qubits to a quantum system doesn't always improve performance. The effectiveness of additional Qubits depends on the quantum algorithm and how well it matches the dataset. Additionally, we examine the effects of varying entangling layers on entanglement entropy and test accuracy. The performance of Laplacian learning is highly dependent on the number of entangling layers, with optimal configurations varying across different datasets. Typically, moderate levels of entanglement offer the best balance between model complexity and generalization capabilities. These observations highlight the crucial need for precise hyperparameter tuning tailored to each dataset to achieve optimal performance in Laplacian learning methods.

A preprocessing perspective for quantum machine learning classification advantage using NISQ algorithms

Quantum Machine Learning (QML) hasn't yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved small incremental advantages, and a few experimental cases in hybrid quantum computing are promising considering a mid-term future (not taking into account the achievements purely associated with optimization using quantum-classical algorithms). The current quantum computers are noisy and have few qubits to test, making it difficult to demonstrate the current and potential quantum advantage of QML methods. This study shows that we can achieve better classical encoding and performance of quantum classifiers by using Linear Discriminant Analysis (LDA) during the data preprocessing step. As a result, Variational Quantum Algorithm (VQA) shows a gain of performance in balanced accuracy with the LDA technique and outperforms baseline classical classifiers.