Frequency-Domain Analysis of Time-Dependent Multiomic Data in Progressive Neurodegenerative Diseases: A Proposed Quantum-Classical Hybrid Approach with Quaternionic Extensions

• URL: http://arxiv.org/abs/2508.07948v1
• Date: Mon, 11 Aug 2025 13:03:58 GMT
• Title: Frequency-Domain Analysis of Time-Dependent Multiomic Data in Progressive Neurodegenerative Diseases: A Proposed Quantum-Classical Hybrid Approach with Quaternionic Extensions
• Authors: John D. Mayfield M. D. Ph. D. M. Sc,
• Abstract summary: We propose a theoretical mathematical framework that transforms time-series data into frequency or s-domain.<n>We employ quantum-classical hybrid computing with variational quantum eigensolvers (VQE) for enhanced pattern detection.<n>This framework aims to lay the groundwork for redefining precision medicine for neurodegenerative diseases through future validations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Progressive neurodegenerative diseases, including Alzheimer's disease (AD), multiple sclerosis (MS), Parkinson's disease (PD), and amyotrophic lateral sclerosis (ALS), exhibit complex, nonlinear trajectories that challenge deterministic modeling. Traditional time-domain analyses of multiomic and neuroimaging data often fail to capture hidden oscillatory patterns, limiting predictive accuracy. We propose a theoretical mathematical framework that transforms time-series data into frequency or s-domain using Fourier and Laplace transforms, models neuronal dynamics via Hamiltonian formulations, and employs quantum-classical hybrid computing with variational quantum eigensolvers (VQE) for enhanced pattern detection. This theoretical construct serves as a foundation for future empirical works in quantum-enhanced analysis of neurodegenerative diseases. We extend this to quaternionic representations with three imaginary axes ($i, j, k$) to model multistate Hamiltonians in multifaceted disorders, drawing from quantum neuromorphic computing to capture entangled neural dynamics \citep{Pehle2020, Emani2019}. This approach leverages quantum advantages in handling high-dimensional amplitude-phase data, enabling outlier detection and frequency signature analysis. Potential clinical applications include identifying high-risk patients with rapid progression or therapy resistance using s-domain biomarkers, supported by quantum machine learning (QML) precedents achieving up to 99.89% accuracy in Alzheimer's classification \citep{Belay2024, Bhowmik2025}. This framework aims to lay the groundwork for redefining precision medicine for neurodegenerative diseases through future validations.

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