Control-Anchored QUBO Clustering Reveals Control-Distant Postural Control Patterns in Motion Capture Balance Signals After COVID-19

Post-COVID-19 balance and postural control alterations have been reported after SARS-CoV-2 infection, but individual-level phenotyping remains challenging because post-acute sequelae are heterogeneous and often lack clear clinical ground truths. We analyzed motion capture balance data from 140 participants, including 114 post-COVID-19 participants and 26 control-group participants, who completed sensory organization/postural balance tasks under single-task and cognitive dual-task conditions. Relative joint angle trajectories were transformed into 0-5 Hz frequency-domain spectra, from which 13 balance-derived task contrasts were constructed to capture cognitive dual-task versus single-task differences, closed-eyes versus open-eyes task condition differences, and related task condition changes. Joint-wise spectral contrast features were encoded using a vector-quantized variational autoencoder. Control-distant subgroup discovery was then formulated as a control-anchored, graph-based QUBO clustering problem and solved using a quantum annealing workflow. Simulated annealing and tabu search were applied to the identical BQM/QUBO formulation as classical solver-level references, whereas Gaussian mixture modeling was retained as an unconstrained classical clustering reference. Consistent with the control-anchored design of the QUBO objective, QUBO clustering identified a selective subset of post-COVID-19 participants with control-distant latent balance profiles while largely preserving the control-group reference structure. Across all task contrasts, quantum annealing assigned 1 of 307 control-group participant-contrast assignments (0.3%) and 118 of 1366 post-COVID-19 participant-contrast assignments (8.6%) to the control-distant group. Simulated annealing and tabu search produced slightly larger but similar control-distant post-COVID-19 subsets, assigning 143 of 1366 post-COVID participant-contrast assignments (10.5%) and 0 of 307 control-group participant-contrast assignments (0.0%) to the control-distant group. In contrast, GMM assigned 63 of 307 control-group participant-contrast assignments (20.5%) and 266 of 1366 post-COVID-19 participant-contrast assignments (19.5%) to the control-distant group. Parameter sensitivity analysis showed high overall assignment agreement for the same BQM/QUBO formulation, but the exact membership of the sparse control-distant subset was more variable. Simulated annealing sensitivity analysis showed overall agreement of 98.3-100.0% and control-distant Jaccard indices of 0.836-1.000 relative to the baseline, whereas a representative QPU sensitivity analysis showed overall agreement of 93.6-100.0% and control-distant Jaccard indices of 0.443-1.000. Frequency band profiles further suggested that QUBO-derived control-distant assignments corresponded to contrast-dependent and exploratory interpretable postural control patterns, particularly in low-frequency postural sway-dominant and mid-low-frequency postural control bands. These findings support the feasibility of objective-driven, control-anchored QUBO-based quantum-assisted clustering for exploratory subgroup discovery in heterogeneous, label-limited biomedical datasets. The proposed framework does not establish diagnostic criteria for long COVID or evidence of quantum speedup but provides a hypothesis-generating approach for interpretable post-COVID-19 neuromotor phenotyping and related medical data analysis applications.