Here is a list of good QLDPC codes.
| Code | Description |
|---|---|
| Dinur-Hsieh-Lin-Vidick (DHLV) code | Stub. |
| Expander LP code | Family of \(G\)-lifted product codes constructed using two random classical Tanner codes defined on expander graphs [1]. For certain parameters, this construction yields the first asymptotically good QLDPC codes. Classical codes resulting from this construction are one of the first two families of \(c^3\)-LTCs. |
| Lossless expander balanced-product code | 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 [2] yields a \(c^3\)-LTC [3]. Using two-sided expanders, which are only conjectured to exist, yields an asymptotically good QLDPC code family [4]. |
| Quantum Tanner code | Member of a family of QLDPC codes based on two compatible classical Tanner codes defined on a two-dimensional Cayley complex. For certain choices of codes and complex, the resulting codes have asymptotically good parameters. |
| Topological code | A code whose codewords form the ground-state or low-energy subspace of a code Hamiltonian realizing a topological phase. A topological phase may be bosonic or fermionic, i.e., constructed out of underlying subsystems whose operators commute or anti-commute with each other, respectively. Unless otherwise noted, the phases discussed are bosonic. |
References
- [1]
- S. Hoory, N. Linial, and A. Wigderson, “Expander graphs and their applications”, Bulletin of the American Mathematical Society 43, 439 (2006) DOI
- [2]
- 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
- [3]
- T.-C. Lin and M.-H. Hsieh, “\(c^3\)-Locally Testable Codes from Lossless Expanders”, (2022) arXiv:2201.11369
- [4]
- T.-C. Lin and M.-H. Hsieh, “Good quantum LDPC codes with linear time decoder from lossless expanders”, (2022) arXiv:2203.03581