Hyperbolic Floquet code[13] 

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 depolarising 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”, (2023) arXiv:2309.10033
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Zoo Code ID: hyperbolic_floquet

Cite as:
“Hyperbolic Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/hyperbolic_floquet
BibTeX:
@incollection{eczoo_hyperbolic_floquet, title={Hyperbolic Floquet code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/hyperbolic_floquet} }
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Permanent link:
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Cite as:

“Hyperbolic Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/hyperbolic_floquet

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/dynamic/floquet/hyperbolic_floquet.yml.