QBayMic: Quantum-coupled variational Bayes for clustering and feature selection in low-signal microbiome data

ABSTRACT Clustering microbiome samples into community types is central to cohort stratification and biomarker discovery, yet the resulting inference becomes unstable when the between-group signal is small compared with sampling noise: variational Bayes yields different partitions across initialisations, and commonfixes do not solve the problem. Simple restarts are ineffective because the variational free energy is anti-correlated with clustering accuracy; deterministic annealing collapses to the same solution as greedy ascent, with the operator staying diagonal at every temperature; and parallel-tempering replicas remain too similar to permit configuration exchanges. We propose QBayMic, which replaces the assignment step of a Dirichlet-multinomial mixture with sparse variable selection via a quantum Gibbs state under an annealed Hamiltonian, coupling competing assignments through a transverse-field term that cannot be reproduced by temperature scaling alone. We present two gate-based circuit designs for this step, evaluating on noiseless qubit-register simulations, and we derive a signal fraction σ , computable prior to clustering, that predicts the expected strength of quantum coupling. With matched compute in the predicted regime, the three classical methods recovered the reference partition (ARI > 0.4) in 0/100 seeds, while QBayMic recovered it in 47–64/100; when the number of clusters exceeded three, only QBayMic recovered the correct cluster count. For a soil pH dataset, the diagnostic indicates a narrow separation margin; for a human-derived dataset tuned into the predicted band via controlled dilution, classical methods recovered the cluster count in 0/100 seeds, compared with 61–76% for QBayMic. The implementation is publicly available at https://github.com/tungtokyo1108/QBayMic .