## Description

QLDPC code constructed by taking the balanced product of lossless expander graphs. Using one part of a quantum-code chain complex constructed with one-sided loss expanders [3] yields a \(c^3\)-LTC [1]. Using two-sided expanders, which are only conjectured to exist, yields an asymptotically good QLDPC code family [2].

## Rate

Asymptotically good QLDPC codes [2], assuming the existence of two-sided lossless expanders.

## Parents

## Cousins

- Locally testable code (LTC) — Using one part of a quantum-code chain complex constructed with one-sided loss expanders yields a \(c^3\)-LTC [1].
- Good QLDPC code — Taking a balanced product of two-sided expanders, which are only conjectured to exist, yields an asymptotically good QLDPC code family [2].

## References

- [1]
- T.-C. Lin and M.-H. Hsieh, “\(c^3\)-Locally Testable Codes from Lossless Expanders”, (2022) arXiv:2201.11369
- [2]
- T.-C. Lin and M.-H. Hsieh, “Good quantum LDPC codes with linear time decoder from lossless expanders”, (2022) arXiv:2203.03581
- [3]
- M. Capalbo et al., “Randomness conductors and constant-degree lossless expanders”, Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC ’02 (2002) DOI

## Page edit log

- Victor V. Albert (2023-05-10) — most recent

## Cite as:

“Lossless expander balanced-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/lossless_expander