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\([[17,1,5]]\) 4.8.8 color code[1]

Description

Seventeen-qubit doubly even 2D color code that admits a transversal implementation of the logical Clifford group.

Encoding

Fault-tolerant logical zero state preparation using reinforcement learning [2].

Transversal Gates

Transversal implementation of the logical Clifford group.

Fault Tolerance

Fault-tolerant logical zero state preparation using reinforcement learning [2].

Cousin

  • \([[49,1,5]]\) triorthogonal code— The \([[49,1,5]]\) triorthogonal code can be viewed as a (gauge-fixed) doubled color code obtained from the \([[17,1,5]]\) 4.8.8 color code via the doubling transformation [3].

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
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Quantum rainbow code
Quantum pin codeStabilizer Hamiltonian-based Qubit QECC Quantum
Color code
2D color codeGeneralized homological-product Twist-defect color Lattice stabilizer QLDPC CSS Stabilizer Qubit Abelian topological Topological Hamiltonian-based QECC Quantum
Square-octagon (4.8.8) color code
Parents
Square-octagon (4.8.8) color code
Quantum divisible codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[17,1,5]]\) 4.8.8 color code

References

[1]
H. Bombin and M. A. Martin-Delgado, “Topological Quantum Distillation”, Physical Review Letters 97, (2006) arXiv:quant-ph/0605138 DOI
[2]
R. Zen, J. Olle, L. Colmenarez, M. Puviani, M. Müller, and F. Marquardt, “Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning”, (2024) arXiv:2402.17761
[3]
S. Bravyi and A. Cross, “Doubled Color Codes”, (2015) arXiv:1509.03239
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Zoo Code ID: stab_17_1_5

Cite as:
“\([[17,1,5]]\) 4.8.8 color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/stab_17_1_5
BibTeX:
@incollection{eczoo_stab_17_1_5, title={\([[17,1,5]]\) 4.8.8 color code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_17_1_5} }
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Permanent link:
https://errorcorrectionzoo.org/c/stab_17_1_5

Cite as:

“\([[17,1,5]]\) 4.8.8 color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/stab_17_1_5

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/color/stab_17_1_5.yml.