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Stochastic Entanglement Configuration for Constructive Entanglement Topologies in Quantum Machine Learning with Application to Cardiac MRI

Efficient entanglement strategies are essential for advancing variational quantum circuits (VQCs) for quantum machine learning (QML). However, most current approaches use fixed entanglement topologies that are not adaptive to task requirements, limiting potential gains over classical models. We introduce a novel stochastic entanglement configuration method that systematically generates diverse entanglement topologies to identify a subspace of constructive entanglement configurations, defined as entanglement topologies that boost hybrid model performance (e.g., classification accuracy) beyond classical baselines. Each configuration is encoded as a stochastic binary matrix, denoting directed entanglement between qubits. This enables scalable exploration of the hyperspace of candidate entanglement topologies using entanglement density and per-qubit constraints as key metrics. We define unconstrained and constrained sampling modes, controlling entanglement per qubit. Using our method, 400 stochastic configurations were generated and evaluated in a hybrid QML for cardiac MRI disease classification. We identified 64 (16%) novel constructive entanglement configurations that consistently outperformed the classical baseline. Ensemble aggregation of top-performing configurations achieved ~0.92 classification accuracy, exceeding the classical model (~0.87) by over 5%. Compared to four conventional topologies (ring, nearest neighbor, no entanglement, fully entangled), none surpassed the classical baseline (maximum accuracy ~0.82), while our configurations delivered up to ~20% higher accuracy. Thus, highlighting the robustness and generalizability of the identified constructive entanglements.

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