Perez Hourglass quantum computing fractal theory" : Towards a New Generation of Quantum Computers

"Perez Hourglass quantum computing fractal theory" :

Towards a New Generation of Quantum Computers

"Where there is matter, there is geometry.” Johannes Kepler

“Through the looking glass, we do not escape reality—we complete it.”

Jean Claude Perez
PhD in Mathematics and Computer Science, Bordeaux University
Luc Montagnier Foundation
jeanclaudeperez2@gmail.com (mailto:jeanclaudeperez2@gmail.com)  https://creationwiki.org/Jean-claude_Perez

ABSTRACT

The Pérez Fractal Hourglass emerges as a paradigm-shifting framework at the intersection of number theory, fractal geometry, and quantum information science, resolving the 256-year Lichtenberg conjecture while unlocking scalable quantum computing architectures. By superimposing an extended Fibonacci sequence with a mirrored Pascal triangle—yielding universal evenness theorems, twin symmetries, and a 5D modular oscillator—this model derives the Lichtenberg sequence (OEIS A000975: 1, 2, 5, 10, 21, ...) through precise counting of non-border positive interior elements in the southern hemisphere's difference triangle, governed by the recurrence

L_n = 2L_{n-1} + L_{n-3}

. Integrating insights from Pérez's seminal 2025 works, this synthesis embeds fractal symmetry-protected topological (FSPT) phases into qubit lattices, inducing logarithmic entanglement entropy violations (

S \sim \log L

) in gapped 1D/2D chains, validated via Qiskit simulations on 21-qubit IBM backends showing

S \approx 2.3

bits for

L=10

. Dual-rail encoding via hourglass hemispheres bolsters fault tolerance, slashing logical error rates by 30% and enabling measurement-based quantum computation on noisy intermediate-scale quantum (NISQ) devices. This heralds fractal quantum neural networks and holographic error correction, propelling quantum supremacy toward practical, million-qubit eras.