Dinur-Hsieh-Lin-Vidick (DHLV) code[1]
Description
A family of asymptotically good QLDPC codes which are related to expander LP codes in that the roles of the check operators and physical qubits are exchanged.Rate
Asymptotically good QLDPC codes.Decoding
Linear-time decoder utilizing the small set-flip decoder [2] for \(Z\) errors and a reconstruction procedure for \(X\) errors [1].Cousins
- Good QLDPC code— DHLV code construction yields asymptotically good QLDPC codes.
- Regular binary Tanner code— Regular binary Tanner codes are used in constructing quantum DHLV codes.
- Tensor-product code— Tensor codes are used in constructing quantum DHLV codes.
- Balanced product (BP) code— DHLV codes can be obtained from a balanced product of two expander codes [3].
Primary Hierarchy
Generalized homological-product qubit CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Parents
Lifted-product (LP) codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
DHLV codes are LP codes [3; Footnote 7].
Dinur-Hsieh-Lin-Vidick (DHLV) code
References
- [1]
- I. Dinur, M.-H. Hsieh, T.-C. Lin, and T. Vidick, “Good Quantum LDPC Codes with Linear Time Decoders”, (2022) arXiv:2206.07750
- [2]
- S. Gu, C. A. Pattison, and E. Tang, “An efficient decoder for a linear distance quantum LDPC code”, (2022) arXiv:2206.06557
- [3]
- P. Panteleev and G. Kalachev, “Maximally Extendable Sheaf Codes”, (2024) arXiv:2403.03651
Page edit log
- Victor V. Albert (2022-06-17) — most recent
Cite as:
“Dinur-Hsieh-Lin-Vidick (DHLV) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dhlv