Quantum check-product code[1]
Description
CSS code constructed from an extension of check product (between two classical codes) to a product between a classical and a quantum code.
Parents
- Generalized homological-product qubit CSS code
- Quantum locally testable code (QLTC) — Quantum check-product constructions yield an sLTC code with constant soundness \(2\rho\) from a classical LTC code with soundness \(\rho\) [1]. While these are the first bona-fide QLTC code family because they admit asymptotically constant soundness, they are not practical because their distance is two.
Cousins
- Tensor-product code — Quantum check-product codes extend the concept of a check product, which yields the dual of a tensor code, to a product between a classical and a quantum code.
- Quantum tensor-product code — Quantum check-product codes extend the concept of a check product, which yields the dual of a tensor code, to a product between a classical and a quantum code.
- Distance-balanced code — Quantum check-product code constructions use distance balancing to increase distance [1].
References
- [1]
- A. Cross et al., “Quantum Locally Testable Code with Constant Soundness”, (2023) arXiv:2209.11405
Page edit log
- Victor V. Albert (2022-09-26) — most recent
Cite as:
“Quantum check-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/check_product