2D Tile codes

Tile codes are generalization of surface codes that offers flexibility in terms of locality and stabilizer weight without compromising 2D locality with open boundary conditions. These codes outperform surface codes and planar versions of bivariate bicycle codes. BB codes have a modest amount of non-locality because of periodic boundary conditions of the 2D lattice. These hardware issues caused by non-locality has been recently addressed in new layout such as [here](https://quantum-journal.org/papers/q-2025-05-05-1728/ ) or other means. Nevertheless, if we want to avoid the assumption of periodic boundary conditions, tile codes present an new venue of code design with open boundary conditions. The rates of these codes is not that high compared to some other codes. However, they offer the following benefit: > Tile codes do not require periodicity and thus have true O(1)-locality on a planar 2D lattice. With that, tile codes address this major challenge in quantum error correction, achieving high efficiency while preserving implementability on near-term hardware. Implementing it would be valuable for comparison with other classes of modern error correcting codes. reference: https://arxiv.org/pdf/2504.09171