Subsystem color code[1,2] 






  • Color code
  • Symmetry-protected self-correcting quantum code — A particular gauge-fixed version of this code on a 3D lattice yields a self-correcting memory protected by one-form symmetries (see Sec. IV D of Ref. [3]). The symmetric energy barrier grows linearly with the length of a side of the lattice. When the system is coupled locally to a thermal bath respecting the symmetry and below a critical temperature, the memory time grows exponentially with the side length. The gauge color code is not a self-correcting quantum memory if symmetry protection is removed [4].
  • Honeycomb Floquet code — Both honeycomb and subsystem color codes are generated via periodic sequences of measurements. However, any measurement sequence can be performed on the color code without destroying the logical qubits, while honeycomb codes can be maintained only with specific sequences. Honeycomb codes require a shorter measurement cycle and use fewer qubits at the given code distance [5].
  • Raussendorf-Bravyi-Harrington (RBH) cluster-state code — The RBH code for a certain boundary Hamiltonian is dual to the gauge color code [3; Sec. IV.C.1].


H. Bombin, “Topological subsystem codes”, Physical Review A 81, (2010) arXiv:0908.4246 DOI
H. Bombin, “Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes”, (2015) arXiv:1311.0879
S. Roberts and S. D. Bartlett, “Symmetry-Protected Self-Correcting Quantum Memories”, Physical Review X 10, (2020) arXiv:1805.01474 DOI
Y. Li et al., “Phase diagram of the three-dimensional subsystem toric code”, (2023) arXiv:2305.06389
M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021) arXiv:2107.02194 DOI
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Zoo Code ID: subsystem_color

Cite as:
“Subsystem color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
  title={Subsystem color code},
  booktitle={The Error Correction Zoo},
  editor={Albert, Victor V. and Faist, Philippe},
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“Subsystem color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.