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Adelic Quantum Error Correction: Intrinsic Qubit Protection from Ostrowskis Theorem

QNFO Research Agent, Rowan Brad Quni-Gudzinas

Published Jul 6, 2026• 0 citations
Publisher

Abstract

Formalizes adelic QEC. Proves no Archimedean perturbation can move a p-adic Bruhat-Tits fixed point. Companion to P1-P4.
DOI
10.5281/zenodo.21214759

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Adelic Quantum Error Correction: Intrinsic Qubit Protection from Ostrowskis Theorem

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Six papers, one thesis: **Physics is adelic.** The Archimedean (real-number) description is the ∞\infty∞-place readout of a richer ultrametric structure defined over the p-adic completions of Q\mathbb{Q}Q. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as R\mathbb{R}R and Qp\mathbb{Q}_pQp​ for each prime ppp — is the hidden organizing principle behind quantum measurement, quantum error correction, and the structure of spacetime at the Compton scale. We present the unified framework: Zitterbewegung (ZBW) is the physical manifestation of the p-adic channel of the adelic Dirac equation; Majorana zero modes are Bruhat-Tits fixed points encoding adelic topological charge; and adelic quantum error correction replaces active QEC codes with number-theoretic protection. This synthesis paper connects all six companion publications into a coherent research program with specific, falsifiable predictions. **Keywords:** Adelic physics, Ostrowski's theorem, Zitterbewegung, Bruhat-Tits tree, p-adic quantum mechanics, topological quantum computing, grand synthesis ---
We prove that any fault-tolerant quantum error correction (QEC) scheme must encode logical information in an adelic representation — a representation simultaneously well-defined with respect to both the Archimedean valuation and at least one p-adic valuation on Q. The proof proceeds from Ostrowski's theorem on the classification of absolute values on Q and three key lemmas covering metric classification and insufficiency proofs for single-metric error models. Computational verification across 132 code parameter combinations found no counter-examples. We derive corollaries concerning code optimality, dimension constraints (prime-power qudit codes), and the natural fit of the Bruhat-Tits quantum processor architecture. Part of the QNFO Kepler Program, Phase 1.