This preprint introduces Quantum Hidden Variable Extraction (Q-HVE), a quantum algorithm that applies Grover-style amplitude amplification to identify which hidden-variable model best explains residual signal in a dataset after classical baselines have been subtracted. The algorithm achieves an unconditional O(√m) quadratic speedup over classical sequential model evaluation for libraries of m candidate models. The work argues that the four XPRIZE Quantum Applications problem domains — human health, climate science, energy systems, and materials engineering — share a common epistemic defect: their classical baseline models systematically exclude documented hidden variables. The Presignal Research Initiative has identified those variables across its published portfolio. Q-HVE provides the quantum acceleration layer that makes rapid model selection over those libraries computationally feasible. The four instantiations are: (1) Immunological Tinnitus Subtype (ITS), supported by peer-reviewed meta-analysis and active clinical trials; (2) heliospheric-ISM climate forcing, supported by published astrophysical modeling and isotopic evidence; (3) Vertical Arcology Hydraulic Spine (VAHS), a conceptual high-head pumped storage architecture; and (4) transport-regime-optimal battery electrode porosity derived from generalized Murray's Law. Epistemic status is explicitly graded for each domain. Resource estimates indicate Q-HVE is practical on a fault-tolerant quantum computer with approximately 85 logical qubits. No new experimental data are presented. This is a theoretical proposal posted for public scientific scrutiny under CC BY 4.0.
John Carter (Mon,) studied this question.