\([[8,3,2]]\) CSS code[1,2] 

Also known as Smallest interesting color code.


Smallest 3D color code whose physical qubits lie on vertices of a cube and which admits a transversal CCZ gate.

Transversal Gates

CZ gates between any two logical qubits [3] and CCZ gate [13].

Fault Tolerance

CCZ gate can be distilled in a fault-tolerant manner [4].


Trapped ions: one-qubit addition algorithm implemented fault-tolerantly on the Quantinuum H1-1 device [5].Superconducting circuits: fault-tolerant \(CZZ\) gate performed on IBM and IonQ devices [6].Rydberg atom arrays: Lukin group [7]. 48 logical qubits, 228 logical two-qubit gates, 48 logical CCZ gates, and error detection peformed in 16 blocks. Circuit outcomes were sampled and cross-entropy (XEB) was calculated to verify quantumness. Logical entanglement entropy was measured [8].




A. Kubica, B. Yoshida, and F. Pastawski, “Unfolding the color code”, New Journal of Physics 17, 083026 (2015) arXiv:1503.02065 DOI
E. Campbell, “The smallest interesting colour code,” Online available at https://earltcampbell.com/2016/09/26/the-smallest-interesting-colour-code/ (2016), accessed on 2019-12-09.
H. Chen et al., “Automated discovery of logical gates for quantum error correction (with Supplementary (153 pages))”, Quantum Information and Computation 22, 947 (2022) arXiv:1912.10063 DOI
J. Haah and M. B. Hastings, “Measurement sequences for magic state distillation”, Quantum 5, 383 (2021) arXiv:2007.07929 DOI
Y. Wang et al., “Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code”, (2023) arXiv:2309.09893
D. H. Menendez, A. Ray, and M. Vasmer, “Implementing fault-tolerant non-Clifford gates using the [[8,3,2]] color code”, (2023) arXiv:2309.08663
Q. Xu et al., “Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays”, (2023) arXiv:2308.08648
D. Bluvstein et al., “Logical quantum processor based on reconfigurable atom arrays”, Nature (2023) arXiv:2312.03982 DOI
M. Vasmer and A. Kubica, “Morphing Quantum Codes”, PRX Quantum 3, (2022) arXiv:2112.01446 DOI
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Zoo Code ID: stab_8_3_2

Cite as:
\([[8,3,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/stab_8_3_2
@incollection{eczoo_stab_8_3_2, title={\([[8,3,2]]\) CSS code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_8_3_2} }
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Cite as:

\([[8,3,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/stab_8_3_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/stab_8_3_2.yml.