Overlapped-repetition Shor codes achieving fourfold asymptotic rate

TL;DR

This paper introduces overlapped-repetition Shor codes that significantly improve asymptotic rate while maintaining low stabilizer weight, with extensions to LDPC, bosonic encodings, and error suppression.

Contribution

It presents a novel overlapped-repetition coding scheme achieving fourfold rate improvement and extends the framework to LDPC, bosonic codes, and error suppression techniques.

Findings

Achieves fourfold asymptotic rate improvement.

Maintains average stabilizer weight of 4.

Extends to bosonic oscillator encodings.

Abstract

Introducing controlled overlap among a few repetition blocks yields a fourfold asymptotic rate improvement while preserving an average stabilizer weight of \(4\). Substituting the overlapped outer layer with an LDPC code further produces a family of constructions with asymptotic rate \(2/d\). We also describe a constant-excitation variant that suppresses collective coherent errors without additional overhead, as well as a bosonic generalization that extends the framework to oscillator encodings. The resulting family achieves a code rate intermediate between that of the rotated surface code (average stabilizer weight \(4\)) and the BB code (average stabilizer weight \(6\)), while remaining free of the performance degradation typical of iterative decoders.