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| Main Author: | |
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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.19959267 |
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Table of Contents:
- <p class="p1">We introduce a concatenated quantum error-correcting code construction on the Q3</p> <p class="p2">hypercube graph (the face-adjacency graph of the regular octahedron) with three structural</p> <p class="p3">properties not jointly present in existing constructions: (i) a topologically-protected outer</p> <p class="p1"><span class="s1">Z</span><span class="s2">2 </span>layer enforced by the channel dynamics rather than by an additional encoding step,</p> <p class="p1">(ii) active verification semantics in which the channel performs parity-check measurement</p> <p class="p1">during propagation rather than only at decoding, and (iii) a closed-form channel-friction</p> <p class="p2"><span class="s3">relation </span><span class="s1">M</span><span class="s3">= </span><span class="s1">exp</span><span class="s3">(</span><span class="s1">φF/</span><span class="s3">2), with </span><span class="s1">φ</span><span class="s3">= (</span><span class="s1">√5−</span><span class="s3">1)</span><span class="s1">/</span><span class="s3">2, mapping codeword frustration to an effective</span></p> <p class="p2"><span class="s3">propagation cost. The outer </span><span class="s1">Z</span><span class="s2">2 </span><span class="s3">protection follows from a finite-symmetry theorem on the walk</span></p> <p class="p2"><span class="s3">operator: bit-flipsoftheouter-codebitareforbiddenatallordersbytherotationalstructureof</span></p> <p class="p2"><span class="s3">the bridge dynamics. We prove the theorem, characterise the code’s distance structure under</span></p> <p class="p3"><span class="s1">the concatenated decomposition, and show that the channel-friction relation is the unique</span></p> <p class="p1">fixed point of the walk’s iterative mass-transfer recursion. As a long-form application, we</p> <p class="p2"><span class="s3">map the construction onto the Standard Model fermion content and derive the CKM mixing</span></p> <p class="p1">hierarchy as a code-distance phenomenon, with the ratio <span class="s1">|V</span><span class="s2">ub</span><span class="s1">|/|V</span><span class="s2">cb</span><span class="s1">|≈</span>0<span class="s1">.</span>1 recovered from</p> <p class="p2"><span class="s3">the double-spectral-gap activation threshold for outer-code transitions, matching experiment</span></p> <p class="p3">without fitted parameters. The Standard Model identification is presented as evidence for</p> <p class="p3"><span class="s1">the construction’s physical relevance; the cs.IT results are independent of it.</span></p>