aqora

Quantum Error-Correcting Codes from Algebraic Curves

Jon-Lark Kim, Gretchen L. Matthews

Series on coding theory and cryptologyOct 1, 200813 citations

A Kodaira-Neron Classification of Quantum Error-Correcting Codes

QNFO Research Collective, Rowan Brad Quni-Gudzinas

We establish a precise mathematical correspondence between the classification of quantum CSS stabilizer codes and the Kodaira-Neron classification of elliptic curves over p-adic fields. The stabilizer lattice of a CSS code defines a filtered (phi,N)-module over Q_p whose reduction type determines the code's error-correcting properties. We verify this classification across 7 code families (100% agreement on KN Propositions 3.1-3.7), present the first explicit construction of a semistable non-crystalline code from the Shor 9-qubit stabilizer monodromy, and catalogue 26 conjectures spanning code distance estimates via Hasse-Weil zeta functions, ultrametric tree structures in error syndromes, and Yamada (1969) weight calibration.We establish a precise mathematical correspondence between the classification of quantum CSS stabilizer codes and the Kodaira-Neron classification of elliptic curves over p-adic fields. The stabilizer lattice of a CSS code defines a filtered (phi,N)-module over Q_p whose reduction type determines the code's error-correcting properties. We verify this classification across 7 code families (100% agreement on KN Propositions 3.1-3.7), present the first explicit construction of a semistable non-crystalline code from the Shor 9-qubit stabilizer monodromy, and catalogue 26 conjectures spanning code distance estimates via Hasse-Weil zeta functions, ultrametric tree structures in error syndromes, and Yamada (1969) weight calibration.

Jul 4, 20260 citations

p-Adic Quantum Error Correction Classifier Verification: A Computational Methodology

Rowan Brad Quni-Gudzinas

Computational methodology for verifying three conjectures connecting p-adic valuation to quantum error-correcting code classification: CSS-Ultrametric Correspondence, Kodaira-Neron fibre classification, Mahler v_p-spectral decomposition. 5-month protocol, 1000+ codes, Cloudflare Workers infrastructure with D1/R2/Vectorize.

Jul 30, 20260 citations

Quantum codes from a new construction of self-orthogonal algebraic geometry codes

Fernando Hernando, Gary McGuire, Francisco Monserrat +1 more

arXiv:1907.05645Quantum Information ProcessingFeb 17, 202018 citations

Homological quantum error correcting codes and real projective space

Vivien Londe

Homological quantum error correcting codes and real projective space

Apr 23, 20170 citations