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.
- Topological code— DHLV codes are expected to realize topological quantum spin glass order [3].
Primary Hierarchy
Generalized homological-product qubit CSS codeQLDPC Qubit CSS Generalized homological-product Stabilizer Hamiltonian-based QECC Quantum
Parents
Lifted-product (LP) codeGeneralized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
DHLV codes are LP codes that can be obtained from a balanced product of two expander codes [4; 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]
- A. Leverrier, J.-P. Tillich, and G. Zemor, “Quantum Expander Codes”, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science 810 (2015) arXiv:1504.00822 DOI
- [3]
- B. Placke, T. Rakovszky, N. P. Breuckmann, and V. Khemani, “Topological Quantum Spin Glass Order and its realization in qLDPC codes”, (2024) arXiv:2412.13248
- [4]
- P. Panteleev and G. Kalachev, “Maximally Extendable Sheaf Codes”, (2024) arXiv:2403.03651
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2022-06-17)
Cite as:
“Dinur-Hsieh-Lin-Vidick (DHLV) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/dhlv, arXiv:2606.11484