Toward p-adic Quantum Error Correction: The Metric Mismatch Hypothesis

Abstract

We propose that the persistent failure to demonstrate scalable quantum error correction has a structural cause: conventional QEC is built on Archimedean assumptions while the actual error structure of quantum systems may be ultrametric. We develop p-adic stabilizer codes, define a p-adic weight metric, prove a concatenation theorem, and formulate the metric mismatch hypothesis with falsifiable predictions.