Harmonic Quantum Error Correction: A Dissonance-Minimizing Framework from Organized Complexity
Abstract
Current approaches to Quantum Error Correction (QEC), such as Surface Codes and emerging QLDPC architectures, rely on massive physical redundancy to mitigate stochastic decoherence. We propose a paradigm shift based on the Organized Complexity (OC) Framework, positing that quantum errors are not random events but measurable deviations from a number-theoretic order, defined here as “Dissonance.” By mapping qubit states to the Harmonic Divisor Fan (HDF) lattice, we introduce Prime Rank Topology, where valid logical states are locked to Prime Number coordinates (6N ± 1). We derive a modified Hamiltonian incorporating a “Retraction Potential” (VOC ) rooted in the physics of the Blackness Force (U(1)B), formalized as a Stochastic Differential Equation where deterministic retraction dominates noise. In-silico simulations of a Hexagonal Prime Ring topology demonstrate a 96.2% survival rate against high-dissonance noise. Furthermore, we align this topology with industry-standard “Heavy-Hex” lattices, proposing a “Zeta-Doped” metamaterial architecture that physically filters entropy.
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