ca969f32a7689dff5028a6811a406011 biomimetics-10-00516.pdf ca1de5ccfb092d77e713b17a37447176cabd8acc biomimetics-10-00516.pdf 7ad92a10ccfcf2b582e42d2f7619fc2ed07e8e16137fa2f0fafab23b6c572e66 biomimetics-10-00516.pdf Title: NeuroQ: Quantum-Inspired Brain Emulation Subject: Traditional brain emulation approaches often rely on classical computational models that inadequately capture the stochastic, nonlinear, and potentially coherent features of biological neural systems. In this position paper, we introduce NeuroQ a quantum-inspired framework grounded in stochastic mechanics, particularly Nelson’s formulation. By reformulating the FitzHugh–Nagumo neuron model with structured noise, we derive a Schrödinger-like equation that encodes membrane dynamics in a quantum-like formalism. This formulation enables the use of quantum simulation strategies—including Hamiltonian encoding, variational eigensolvers, and continuous-variable models—for neural emulation. We outline a conceptual roadmap for implementing NeuroQ on near-term quantum platforms and discuss its broader implications for neuromorphic quantum hardware, artificial consciousness, and time-symmetric cognitive architectures. Rather than demonstrating a working prototype, this work aims to establish a coherent theoretical foundation for future research in quantum brain emulation. Keywords: quantum-inspired brain emulation; stochastic mechanics; FitzHugh–Nagumo model; neuronal planck constant; hamiltonian simulation Author: Jordi Vallverdú and Gemma Rius Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25; modified using OpenPDF 1.4.2 CreationDate: Thu Aug 7 05:55:35 2025 CEST ModDate: Thu Aug 7 06:38:14 2025 CEST Custom Metadata: yes Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 21 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 4543524 bytes Optimized: no PDF version: 1.5 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- QZJDAI+URWPalladioL-Ital Type 1 Custom yes yes yes 250 0 WBVJKJ+URWPalladioL-Bold Type 1 Custom yes yes yes 251 0 WCLCME+URWPalladioL-Roma Type 1 Custom yes yes yes 252 0 HUSJPF+PazoMath-Italic Type 1 Builtin yes yes yes 340 0 BONYFT+CMSY10 Type 1 Builtin yes yes yes 341 0 GJHHRN+CMEX10 Type 1 Builtin yes yes yes 342 0 SOSTRQ+CMR10 Type 1 Builtin yes yes yes 343 0 RHKYLG+CMMI10 Type 1 Builtin yes yes yes 373 0 JWJPMF+SFTT1000 Type 1 Custom yes yes yes 397 0 VDKJTM+SFTT0900 Type 1 Custom yes yes yes 424 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-09-10 03:08:00 CEST RepresentationInformation: biomimetics-10-00516.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-09-09 11:36:13 CEST Size: 4543524 Format: PDF Version: 1.5 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 598 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: true CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Item: Title: Background and Related Work Children: Item: Title: FitzHugh-Nagumo (FHN) Model Item: Title: Stochastic Mechanics and Nelson's Theory Item: Title: Quantum Neural Models and Existing Approaches Item: Title: Theoretical Framework Children: Item: Title: Mapping FHN Dynamics to Schrödinger-Like Equations Item: Title: Definition of Neuronal Planck Constant () Item: Title: Wave Function and Neural Interpretation Item: Title: Hamiltonian Formulation of Neuron Dynamics Item: Title: Theoretical Validation Levels Item: Title: Full Derivation of a Schrödinger–Type Equation for the Stochastic FitzHugh–Nagumo Model Children: Item: Title: Stochastic FitzHugh–Nagumo Equations Item: Title: Fokker–Planck Representation Item: Title: Nelson’S Stochastic Mechanics Item: Title: Boundary and Initial Conditions Item: Title: Proof-of-Concept Numerical Strategy Item: Title: Quantum Simulation Strategy Children: Item: Title: Quantum State Representation Item: Title: Circuit Implementation Item: Title: Results and Interpretation Item: Title: Reproducibility Item: Title: Implementation Proposal Children: Item: Title: Simulation Architecture Item: Title: Resource Estimations (Qubits, Gate Depth) Item: Title: Example Circuit or Pseudocode Item: Title: Towards Quantum NeuroQ Networks Item: Title: Hybrid Classical–Quantum Architectures Item: Title: Validation and Empirical Testing Children: Item: Title: Estimating from Neural Recordings Item: Title: Testing Coherent Subthreshold Oscillations Item: Title: Experimental Techniques for Model Testing Item: Title: Near-Term Experimental Roadmap Item: Title: Implications and Applications Children: Item: Title: Neuromorphic Quantum Hardware Item: Title: Artificial Consciousness and AGI Item: Title: Philosophical Considerations Item: Title: Causality and Non-Classical Inference Item: Title: Conclusions Item: Title: From Stochastic FitzHugh–Nagumo Dynamics to Schrödinger-Type Equations Children: Item: Title: Appendix: From Stochastic FitzHugh–Nagumo Dynamics to Schrödinger-Type Equations Children: Item: Title: Stochastic FitzHugh–Nagumo Model Item: Title: Fokker–Planck Equation for Joint Density (v,w,t) Item: Title: Nelson’s Mechanics in Multiple Dimensions Item: Title: Madelung Transformation and Neural Wavefunction Item: Title: Interpretation and Simulation Implications Item: Title: References Info: Title: NeuroQ: Quantum-Inspired Brain Emulation Author: Jordi Vallverdú and Gemma Rius Subject: Traditional brain emulation approaches often rely on classical computational models that inadequately capture the stochastic, nonlinear, and potentially coherent features of biological neural systems. In this position paper, we introduce NeuroQ a quantum-inspired framework grounded in stochastic mechanics, particularly Nelson’s formulation. By reformulating the FitzHugh–Nagumo neuron model with structured noise, we derive a Schrödinger-like equation that encodes membrane dynamics in a quantum-like formalism. This formulation enables the use of quantum simulation strategies—including Hamiltonian encoding, variational eigensolvers, and continuous-variable models—for neural emulation. We outline a conceptual roadmap for implementing NeuroQ on near-term quantum platforms and discuss its broader implications for neuromorphic quantum hardware, artificial consciousness, and time-symmetric cognitive architectures. Rather than demonstrating a working prototype, this work aims to establish a coherent theoretical foundation for future research in quantum brain emulation. 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