La-cross code[1]
Description
Code constructed using the hypergraph product of two copies of a cyclic LDPC code. The construction uses cyclic LDPC codes with generating polynomials \(1+x+x^k\) for some \(k\). Using a length-\(n\) seed code yields an \([[2n^2,2k^2]]\) family for periodic boundary conditions and an \([[(n-k)^2+n^2,k^2]]\) family for open boundary conditions.
Parents
- Hypergraph product (HGP) code — La-cross codes are constructed using the hypergraph product a cyclic LDPC code with itself.
- Cyclic quantum code
Cousins
- Long-range enhanced surface code (LRESC) — La-cross codes yield LRESCs for \(k=2\). La-cross codes have a number of long-range stabilizers that scales linearly with code size, while the number of LRESC long-range stabilizers can be tuned to scale between the square-root of the size and linearly in the size.
- Kitaev surface code — La-cross codes at \(k=1\) yield the toric (planar surface) code and periodic (open) boundary conditions.
References
- [1]
- L. Pecorari et al., “High-rate quantum LDPC codes for long-range-connected neutral atom registers”, (2024) arXiv:2404.13010
Page edit log
- Victor V. Albert (2024-04-22) — most recent
Cite as:
“La-cross code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/lacross