A theory of quantum error correction for permutation-invariant codes

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Yingkai Ouyang, Gavin K. Brennen
DOI: 10.48550/arxiv.2602.13638
Cited by: 0

Abstract

We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI code. These algorithms involve measurements of total angular momentum, quantum Schur transforms or logical state teleportations, and geometric phase gates. For erasure errors, or more generally deletion errors, on certain PI codes, we give a simpler quantum error correction algorithm.

Fields of Study & Subjects

Quantum Computing Algorithms and Architecture Quantum Information and Cryptography Coding theory and cryptography

Publication details

Journal / source
arXiv (Cornell University)
Publication date
14 February 2026
Language
EN
Document type
Preprint