https://arxiv.org/pdf/1208.0928 https://arxiv.org/pdf/1208.0928 is a pretty good into to surface codes. https://www.nature.com/articles/s41586-024-08449-y http

https://arxiv.org/pdf/1208.0928 https://arxiv.org/pdf/1208.0928 is a pretty good into to surface codes. https://www.nature.com/articles/s41586-024-08449-y https://www.nature.com/articles/s41586-024-08449-y is a paper that shows surface codes work on real computers. https://arxiv.org/abs/2505.15917v1 https://arxiv.org/abs/2505.15917v1 is the most recent costing of factoring various size of N using all the recent papers on optimizing the logical qbit counts.