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.
  • Honeycomb 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 [4].
  • Raussendorf-Bravyi-Harrington (RBH) code — The RBH code on a certain lattice is dual to the gauge color code.

Zoo code information

Internal code ID: subsystem_color

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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.
@incollection{eczoo_subsystem_color, title={Subsystem color code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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H. Bombin, “Topological subsystem codes”, Physical Review A 81, (2010). DOI; 0908.4246
H. Bombin, “Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes”. 1311.0879
S. Roberts and S. D. Bartlett, “Symmetry-Protected Self-Correcting Quantum Memories”, Physical Review X 10, (2020). DOI; 1805.01474
M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021). DOI; 2107.02194

Cite as:

“Subsystem color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.