Preventive Psychology for Reducing Conversion Risk from Major Depressive Disorder to Bipolar Disorder Type 2: A Hybrid Classical and Quantum Bayesian Simulation Approach

Background & ObjectiveThe conversion from Major Depressive Disorder (MDD) to Bipolar Disorder Type II (BD-II) represents a significant clinical challenge. Longitudinal cohort studies remain the gold standard for estimating the annual conversion rate ( ββ ), but they are costly, time-consuming, and ethically constrained. This study presents a novel probabilistic framework grounded in preventive psychology, establishing exact efficacy thresholds for behavioral interventions without relying on long-term observational cohorts. Methodology & Key ContributionsThis work bridges psychiatric epidemiology and applied computational mathematics through a two-fold approach: Classical Bayesian Simulation: We employed Monte Carlo simulations with literature-calibrated hierarchical Beta priors ( β≈1–2%β≈1–2% per year) alongside MEPS-derived population stratification. A scenario-based sensitivity analysis evaluated hypothetical reductions in ββ (10%, 25%, 40%) to quantify the expected population-level benefits of preventive interventions. Quantum-Ready Computational Framework: Anticipating the limits of classical computing for high-dimensional risk modeling, this study introduces a classically simulated Quantum Amplitude Estimation (QAE) algorithm (Brassard et al., 2002). Built from first principles using standard CPU hardware and NumPy linear algebra, the simulation formally verifies the QAE algorithm’s quadratic query-complexity advantage over classical Monte Carlo ( O(1/M)O(1/M) vs. O(1/M)O(1/M) ). ResultsResults demonstrate that the QAE simulation achieves near-machine-precision ββ estimates ( ∣error∣