Description
Floquet code whose check-operators correspond to edges of a hyperbolic lattice of degree 3.
Protection
Code distance is at most \(O(\log n)\) due to the hyperbolic qubit geometry [1], but semi-hyperbolic lattices yield \(O(\sqrt{n}0\) distance [2].
A useful concept is the embedded distance [2], which is the distance of the stabilizer code lying inside the subspace defined by measurement outcomes of the weight-two parity checks of the code.
Rate
Finite encoding rate whose value depends on the hyperbolic lattice. The asymptotic rate is 1/8 for a lattice of octagons [3].
Decoding
Syndrome structure allows for MWPM decoding.
Threshold
\(0.1\%\) under standard circuit-level depolarizing noise [2].\(0.1\%\) under phenomenological error model including depolarizing and measurement errors for the octagonal codes [3].
Parent
References
- [1]
- C. Vuillot, “Planar Floquet Codes”, (2021) arXiv:2110.05348
- [2]
- O. Higgott and N. P. Breuckmann, “Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes”, (2023) arXiv:2308.03750
- [3]
- A. Fahimniya et al., “Fault-tolerant hyperbolic Floquet quantum error correcting codes”, (2024) arXiv:2309.10033
Page edit log
- Victor V. Albert (2023-10-12) — most recent
- Ali Fahimniya (2023-09-25)
Cite as:
“Hyperbolic Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/hyperbolic_floquet