Citation: Panteleev, Pavel, and Gleb Kalachev. "Asymptotically good quantum and locally testable classical LDPC codes." Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing. 2022.
Web: https://arxiv.org/abs/2111.03654
Tags: Computer-scientific, Error-correcting-codes, Higher-dimensional
This paper is the culmination of a long series of works on quantum error correcting codes. For a long time, people were not able to construct local codes (LDPC codes) with better parameters than the toric code. The toric code encodes L^2 qubits, and has code distance L. This sqrt(N) barrier was finally broken in Freedman's amazing Z2 systolic geometry paper:
> Freedman, Michael H., David A. Meyer, and Feng Luo. "Z2-systolic freedom and quantum codes." Mathematics of quantum computation, Chapman & Hall/CRC (2002): 287-320.
This paper only improved on the toric code by logarithmic factors, however. After a long time of trying, people were eventually able to get full power law savings:
> Hastings, Matthew B., Jeongwan Haah, and Ryan O'Donnell. "Fiber bundle codes: breaking the n 1/2 polylog (n) barrier for quantum ldpc codes." Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. 2021.
After a flurry of work during the pandemic, we were able to go all the way to LDPC codes where are optimal up to scalars. That is the content of this present paper.