Qlustering: Harnessing Network-Based Quantum Transport for Data Clustering

Abstract: We introduce Qlustering, a quantum-inspired algorithm for unsupervised learning that leverages network-based quantum transport to perform data clustering. In contrast to traditional distance-based methods, Qlustering treats the steady-state dynamics of quantum particles propagating through a network as a computational resource. Data are encoded as input states in a tight-binding Hamiltonian framework governed by the Lindblad master equation, and cluster assignments emerge from steady-state output currents at terminal nodes. The algorithm iteratively optimizes the network's Hamiltonian to minimize a physically motivated cost function, achieving convergence through stochastic updates. We benchmark Qlustering on synthetic datasets, a localization problem, and real-world chemical and biological data, namely subsets of the QM9 molecular database and the Iris dataset. Across these diverse tasks, Qlustering demonstrates competitive or superior performance compared with classical methods such as k-means, particularly for non-convex or high-dimensional data. Its intrinsic robustness, low computational complexity, and compatibility with photonic implementations suggest a promising route toward physically realizable, quantum-native clustering architectures.