\([[10,1,2]]\) CSS code[1] 

Description

Smallest stabilizer code to implement a logical \(T\) gate via application of physical \(T\), \(T^{\dagger}\), and \(CCZ\) gates.

Transversal Gates

Logical \(T\) gate via application of physical \(T\), \(T^{\dagger}\), and \(CCZ\) gates [1].

Gates

Magic-state distillation protocol [1].

Fault Tolerance

A fault-tolerant universal gate set can be done via code switching between the Steane code and the \([[10,1,2]]\) code [2].

Realizations

Trapped-ion devices: fault-tolerant universal gate set via code switching between the Steane code and the \([[10,1,2]]\) code on a device from the Monz group [2].

Parents

Cousins

References

[1]
M. Vasmer and A. Kubica, “Morphing Quantum Codes”, PRX Quantum 3, (2022) arXiv:2112.01446 DOI
[2]
I. Pogorelov et al., “Experimental fault-tolerant code switching”, (2024) arXiv:2403.13732
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Zoo Code ID: stab_10_1_2

Cite as:
\([[10,1,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_10_1_2
BibTeX:
@incollection{eczoo_stab_10_1_2, title={\([[10,1,2]]\) CSS code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_10_1_2} }
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https://errorcorrectionzoo.org/c/stab_10_1_2

Cite as:

\([[10,1,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_10_1_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/stab_10_1_2.yml.