Quantum error-correcting codes from Algebraic Geometry codes of Castle type
Carlos Munuera, Wanderson Ten\'orio, Fernando Torres
TL;DR
This paper explores the use of Algebraic Geometry codes, especially Castle codes, to construct quantum error-correcting codes, unifying various known examples under a common theoretical framework.
Contribution
It identifies that many existing quantum codes are Castle codes and provides a systematic theory linking these constructions.
Findings
Many known quantum codes are Castle codes
Unified theory for Castle code-based quantum error correction
Enhanced understanding of algebraic geometric code applications
Abstract
We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this family of codes. We systematize these constructions by showing the common theory that underlies all of them.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.