We introduce , a simple yet powerful way of constructing quantum codes that are local on a planar 2D lattice. Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer weight. Our construction does not compromise on the fact that the codes are local on a lattice with open boundary conditions. Despite its simplicity, we use our construction to find codes with parameters [288,8,12] using weight-6 stabilizers and [288,8,14] using weight-8 stabilizers, outperforming all previously known constructions in this direction. Allowing for a slightly higher nonlocality, we find a [512,18,19] code using weight-8 stabilizers, which outperforms the rotated surface code by a factor of more than 12. Our approach provides a unified framework for understanding the structure of codes that are local on a 2D planar lattice and offers a systematic way to explore the space of possible code parameters. In particular, due to its simplicity, the construction naturally accommodates various types of boundary conditions and stabilizer configurations, making it a versatile tool for quantum error-correction code design.
Steffan et al. (Tue,) studied this question.