ArXiv · 2026
We consider the 4.8.8 color code in a brickwork layout on the square lattice with nearest-neighbor gates. We identify periodic superdense circuits with twelve CNOT layers that appear to preserve the full distance of these codes. Including ancillas, the family uses q=(2d²+5d-5)/2 physical qubits for distance d: asymptotically 2/3 as many as the triangular 6.6.6 color code and 1/2 as many as the rotated surface code at the same code distance. Circuit-level simulations targeting superconducting architectures demonstrate favorable scaling of 4.8.8 color codes at plausible physical noise rates, including both for planar codes and their toroidal cousins under periodic boundary conditions.
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