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arXiv:1402.4370 · Lecture notes in computer science

FPTAS for Weighted Fibonacci Gates and Its Applications

Pinyan Lu, Menghui Wang, Chihao Zhang

Published Jan 1, 2014• 12 citations
arXivHTMLPDF
DOI
10.1007/978-3-662-43948-7_65

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By projecting the 240 E8 roots onto a 2D Fibonacci spiral at 132Hz, we identify three interlocking resonance gates (golden-angle separated at 137.5°) that enforce a topological chirality invariant on any surface code lattice. Error syndromes must cross at least one gate per logical cycle, and the φ-weighted spacing creates an energy gap of exactly 132Hz·φ² ≈ 352Hz that suppresses thermal excitations below threshold. This bridges the E7 phosphorus qubit encoding and the Fibonacci error correction hierarchy by specifying the geometric routing rules that link 128 power-of-2 correction roots to the 112 φ-modulated information roots in a fault-tolerant topology. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
By assigning phi‑weighted Fibonacci coefficients to the 120 antipodal parity bits of the E8 lattice's 240 root vectors, resonant drives at the 132 Hz base frequency generate a hierarchical synchronization that produces protected topological qubit states. The Fibonacci weighting creates a self‑similar coupling pattern that locks the antipodal pair phases into a decoherence‑free subspace, while the harmonic coupling ensures global coherence across the entire lattice. This principle extends the phi‑harmonic synchronization to quantum information, offering a robust platform for E8‑based quantum processors. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Abstract It is an open question if there are leakage-free entangling Fibonacci braiding gates. In this article, we give a construction of a large family of leakage-free braiding gates which are then proved to be non-entangling. We also conducted brute-force numerical searches for braids with a word-length up to seven and found no leakage-free entangling gates. These suggest the negative for the conjecture. On the other hand, we provide a much simpler protocol to generate approximately leakage-free entangling Fibonacci braiding gates than existing algorithms in the literature.