Quantum Hidden Variable Extraction (Q-HVE): A Quadratic-Speedup Quantum Algorithm for Epistemic Noise Subtraction, with Direct Solutions to the XPRIZE Quantum Applications Problem Domains in Health, Climate, Energy, and Materials Science

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.