Layer code[1] 

Description

Member of a family of 3D lattice CSS codes with stabilizer generator weights \(\leq 6\) that are obtained by coupling layers of 2D surface code according to the Tanner graph of a QLDPC code. Geometric locality is maintained because, instead of being concatenated, each pair of parallel surface-code squares are fused (or quasi-concatenated) with perpendicular surface-code squares via lattice surgery.

Rate

Code parameters on a cube, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the 3D BPT bound when asymptotically good QLDPC codes are used in the construction.

Parents

  • Fracton stabilizer code — Layer codes are non-translation invariant 3D lattice stabilizer codes that can be viewed as fracton topological defect networks [1].
  • Abelian topological code — The Layer code realizes 2D layers of \(\mathbb{Z}_2\) gauge theory coupled along defects.

Cousins

  • Good QLDPC code — Layer code parameters, \([[n,\Theta(n^{1/3}),\Theta(n^{1/3})]]\), achieve the BPT bound in 3D when asymptotically good QLDPC codes are used in the construction.
  • Concatenated quantum code — Each pair of surface-code squares in a layer code are fused (or quasi-concatenated) with perpendicular surface-code squares via lattice surgery.
  • Self-correcting quantum code — The energy barrier for layer-code excitations for codes constructed using asymptotically good QLDPC codes scales as \(\Theta{n^{1/3}}\).
  • Kitaev surface code — Layer codes are combinations of constant-rate QLDPC codes with surface codes and build using lattice surgery.

References

[1]
D. J. Williamson and N. Baspin, “Layer Codes”, (2023) arXiv:2309.16503
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Zoo Code ID: layer

Cite as:
“Layer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/layer
BibTeX:
@incollection{eczoo_layer, title={Layer code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/layer} }
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Cite as:

“Layer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/layer

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fracton/layer.yml.