2025/09/11 by Jahan Claes, Claes, Jahan · 1 citation
Computer Science · #Advanced Data Storage Technologies #Cellular Automata and Applications #Computational Geometry and Mesh Generation #FOS: Physical sciences #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2509.09779
openalex publication_date 2025/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The surface code is the most studied error-correcting code thanks to its high threshold, simple decoding, and locality in two dimensions (2D). A key component of any code is its encoding circuit, which maps an unencoded state to the corresponding encoded state. The best previous surface code encoding circuit compatible with 2D local connectivity requires depth 2d to encode distance-d surface codes. This paper presents depth d encoding circuits for the rotated surface code. Our circuit is constructed inductively from circuits that grow the code from d to (d+2). We prove that depth d+O(1) is optimal for inductively constructed circuits.