The surface code is a two-dimensional stabiliser code with parameters [[n,1,Θ(n)]]. To this day, no stabiliser code with growing distance is know to live in less than two dimensions. In this note we show that no such code can exist.
Cite
@article{arxiv.2503.17655,
title = {Stabilizer codes of less than two dimensions have constant distance},
author = {Nouédyn Baspin},
journal= {arXiv preprint arXiv:2503.17655},
year = {2025}
}