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Capped color code (CCC)[1]

Description

A non-geometrically local subsystem color code consisting of two layers of 2D color code stacked together and topped (or capped) by a single qubit. Gauge fixing yields two types of codes, capped color codes in H or T form. Layers of 2D color codes can also be stacked together in a recursive construction, yielding recursive capped color codes (RCCCs).

Transversal and Permutation-Based Gates

Capped color codes in H (T) form admit a transversal Hadamard (T) gate.

Fault Tolerance

Fault-tolerant syndrome extraction and error correction for capped color codes in H form [1].Fault-tolerant T gate implementation [1].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Subsystem qubit codeSubsystem QECC Quantum
Subsystem qubit stabilizer codeSubsystem QECC Quantum
Subsystem qubit CSS codeSubsystem QECC Quantum
Subsystem color codeSubsystem QECC Quantum
Parents
Subsystem color code
Capped color code (CCC)

References

[1]
T. Tansuwannont and D. Leung, “Achieving Fault Tolerance on Capped Color Codes with Few Ancillas”, PRX Quantum 3, (2022) arXiv:2106.02649 DOI
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Zoo Code ID: capped_color

Cite as:
“Capped color code (CCC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/capped_color, arXiv:2606.11484
BibTeX:
@incollection{eczoo_capped_color,
title={Capped color code (CCC)},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/capped_color}
}
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Permanent link:
https://errorcorrectionzoo.org/c/capped_color

Cite as:

“Capped color code (CCC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/capped_color, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/subsystem/topological/color/capped_color.yml.