Long-range enhanced surface code (LRESC)[1]
Description
Code constructed using the hypergraph product of two copies of a concatenated LDPC-repetition seed code. This family interpolates between surface codes and hypergraph codes since the hypergraph product of two repetition codes yields the planar surface code. The construction uses small \([3,2,2]\) and \([6,2,4]\) LDPC codes concatenated with \([4,1,4]\) and \([2,1,2]\) repetition codes, respectively. An example using a \([5,2,3]\) code is also presented.
Gates
Patch-transversal gates for suitable seed codes [1].
Realizations
Preparation of GHZ state of four logical qubits with beyond break-even fidelity in a \([[25,4,3]]\) LRESC [2].
Parent
- Hypergraph product (HGP) code — LRESCs are constructed using the hypergraph product a concatenated LDPC-repetition code with itself.
Cousins
- La-cross code — 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 — LRESCs reduce to planar surface codes when a trivial LDPC code is used in the hypergraph product.
References
- [1]
- Y. Hong et al., “Long-range-enhanced surface codes”, (2024) arXiv:2309.11719
- [2]
- Y. Hong et al., “Entangling four logical qubits beyond break-even in a nonlocal code”, (2024) arXiv:2406.02666
Page edit log
- Victor V. Albert (2024-03-01) — most recent
Cite as:
“Long-range enhanced surface code (LRESC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/lresc