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Stellated color code[1]

Description

A non-CSS color code on a lattice patch with a single twist defect at the center of the patch.

Rate

Stellated color codes have negative curvature around the central defect, and thus circumvent the BPT bound for codes on Euclidean lattices.

Cousin

  • Triangular surface code— Stellated color codes are color-code analogues of triangle surface codes in that both encode logical information in lattices with a single twist defect. Instances of the former can be obtained by fattening [2] the vertices of the latter [1].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Twist-defect color codeLattice stabilizer QLDPC Stabilizer Hamiltonian-based QECC Quantum
Parents
Twist-defect color code
Stellated color code

References

[1]
M. S. Kesselring, F. Pastawski, J. Eisert, and B. J. Brown, “The boundaries and twist defects of the color code and their applications to topological quantum computation”, Quantum 2, 101 (2018) arXiv:1806.02820 DOI
[2]
H. Bombin and M. A. Martin-Delgado, “Exact topological quantum order inD=3and beyond: Branyons and brane-net condensates”, Physical Review B 75, (2007) arXiv:cond-mat/0607736 DOI
Page edit log

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Zoo Code ID: stellated_color

Cite as:
“Stellated color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stellated_color
BibTeX:
@incollection{eczoo_stellated_color, title={Stellated color code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stellated_color} }
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Permanent link:
https://errorcorrectionzoo.org/c/stellated_color

Cite as:

“Stellated color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stellated_color

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/color/non-css/stellated_color.yml.