\([[16,6,4]]\) Tesseract color code[1,2] 

Description

A 4D color code defined on a tesseract, with stabilizer generators of both types supported on each cube.

Decoding

Post-selected fault-tolerant syndrome extraction [1,2].

Fault Tolerance

Post-selected fault-tolerant syndrome extraction [1,2].

Realizations

Trapped-ion devices: logical graph and GHZ states of up to 12 logical qubits constructed using three copies of the tesseract color code, along with five rounds of post-selected fault-tolerant error correction in a device by Quantinuum [3].

Parents

Cousin

References

[1]
N. Delfosse and B. W. Reichardt, “Short Shor-style syndrome sequences”, (2020) arXiv:2008.05051
[2]
P. Prabhu and B. W. Reichardt, “Distance-four quantum codes with combined postselection and error correction”, Physical Review A 110, (2024) arXiv:2112.03785 DOI
[3]
B. W. Reichardt et al., “Demonstration of quantum computation and error correction with a tesseract code”, (2024) arXiv:2409.04628
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Zoo Code ID: stab_16_6_4

Cite as:
“\([[16,6,4]]\) Tesseract color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_16_6_4
BibTeX:
@incollection{eczoo_stab_16_6_4, title={\([[16,6,4]]\) Tesseract color code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_16_6_4} }
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Permanent link:
https://errorcorrectionzoo.org/c/stab_16_6_4

Cite as:

“\([[16,6,4]]\) Tesseract color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_16_6_4

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/color/stab_16_6_4.yml.