Quantum Entropy-Based Clustering for Anomaly Detection in MRI Images Using DQC1

Anomaly detection in high-dimensional fMRI data is hindered by the “curse of dimensionality,” which causes unreliable similarity measures and high computational cost. We present a hybrid quantum entropy-based clustering framework for fMRI anomaly detection that employs the Deterministic Quantum Computation with One Qubit (DQC1) model in unsupervised learning. The method integrates Rényi-2 entropy as a clustering criterion, replacing classical kernel- and density-based entropy estimation with quantum trace-estimation subroutines. Classical MRI features are embedded into quantum states through expressive quantum feature maps, including RY rotations and ZZ-phase entanglement, nonlinear Z–ZZ phase encoding, and compact ZFeatureMap variants, which define quantum kernels measured via DQC1 trace estimation. The framework unifies DQC1-based kernel construction and purity estimation, enabling quantum evaluation of both intra- and inter-cluster entropies. GPU-accelerated simulations using Qiskit Aer GPU, traditional deep learning libraries and also NVIDIA’s cuQuantum librieres demonstrate that DQC1-derived kernels and purity estimators effectively identify anomalous regions with improved separability and reduced complexity, establishing a scalable path toward quantum-assisted medical image clustering.