International Journal of Biomedical Science and Research
The Perez Hourglass: Unifying the Origins of the Universal Ge-netic Code and Opening Pathways to Next-Generation Quan-tum Computing Addendum: Quantum Computing Architec-tures Based on the Perez Hourglass Model
Abstract
Jean-Claude Perez
The Perez Hourglass (Sablier de Perez) is a bidirectional fractal extension of Pascal’s triangle that integrates addition (northern hemisphere), subtraction (southern “antimatter” hemisphere), Fibonacci recursion, golden ratio (φ) harmonics, and the Lichtenberg sequence (OEIS A000975). Through its eight core properties and two pivotal theorems—Theorem 7 on unbreakable parity/symmetry preservation (enabling perfect associative memories and topological protection) and Theorem 8 on the 64 21 unification—it provides a geometric-mathematical explanation for the universal genetic code’s architecture: how 64 (or 128 in double-strand DNA) combinatorial codons compress into 21 functional meanings (20 amino acids + 1 stop). This model suggests a non-random, fractal origin of biological information. An addendum further develops its applications to quantum computing, proposing fractal qubit lattices with golden-ratio-tuned error correction (e.g., distance-3 Fibonacci-valued CSS codes surpassing certain bounds), Perez Hourglass Associative Memory (PHAM) extended to quantum superpositions for noise-resilient storage/retrieval, unbreakable parity-based topological protection (Theorem 7), and logarithmic-depth circuits for fault-tolerant, scalable quantum processors. Together, these elements offer promising blueprints for next-generation quantum computers that mimic biological informational efficiency through fractal symmetry and subtractive refinement.