PreprintarXiv licencearXiv
Denser Planar Color Codes
Abstract
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.
Related
- 4D and 5D Layer Codes through Color Routing
- Algorithmic Construction of Gapped Boundaries for Topological Stabilizer Codes: A Route to Low-Overhead Planar qLDPC Codes
- Circuit-Level Loss Performance of RHG and Foliated Floquet Color Codes in a Compound Photon--Atom Quantum Architecture
- Hyperbolic color codes with constant rate and polynomial distance
- Stitched surface codes: planar concatenation through GHZ corridors
BibTeX
@misc{shutty2026denser,
title = {{Denser Planar Color Codes}},
author = {Noah Shutty},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21376},
eprint = {2609.21376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21376},
}
RIS
TY - UNPB
TI - Denser Planar Color Codes
AU - Noah Shutty
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.21376
UR - https://arxiv.org/abs/2609.21376
AB - 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=(2d^2+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.
ER -