Layer code[1]

Cousins

• Mapping cone code— CSS Layer codes are height-2 mapping cones whose levels are stacks of 2D surface codes and whose string defects implement the chain homotopy; non-CSS Layer codes require the symplectic cone generalization [2,5].
• Abelian topological code— The Layer code realizes 2D layers of \(\mathbb{Z}_2\) gauge theory coupled along defects.
• Fracton stabilizer code— Layer codes are non-translation invariant 3D lattice stabilizer codes that can be viewed as fracton topological defect networks [1].
• Good QLDPC code— Layer codes achieve the 3D BPT bound, with parameters \([[n,\Theta(n^{1/3}),\Theta(n^{2/3})]]\), when asymptotically good QLDPC codes are used in the construction.
• Concatenated qubit code— Each pair of surface-code squares in a layer code is fused (or quasi-concatenated) with perpendicular surface-code squares via lattice surgery.
• Self-correcting quantum code— The energy barrier of excitations for layer codes constructed using asymptotically good QLDPC codes scales as order \(\Theta(n^{1/3})\) [1]. Layer codes are partially self-correcting quantum memories [4,6]. Layer codes constructed from random CSS codes have near-optimal scaling of code parameters and a polynomial energy barrier, exhibiting behavior consistent with partial self-correction [4].
• Kitaev surface code— Layer codes are combinations of constant-rate QLDPC codes with surface codes built using lattice surgery.