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

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

Description

A (self-dual CSS) 4D color code defined on a tesseract, with stabilizer generators of both types supported on each cube. A \([[16,4,2,4]]\) tesseract subsystem code can be obtained from this code by using two logical qubits as gauge qubits [3].

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 \([[16,4,2,4]]\) tesseract subsystem code, along with five rounds of post-selected fault-tolerant error correction in a device by Quantinuum [3].

Parents

Cousins

\([[15, 7, 3]]\) quantum Hamming code — The \([[15,7,3]]\) quantum Hamming code can be obtained by puncturing the tesseract color code [1].
Hypercube code — Stabilizer generators of both types of the tesseract color code are supported on each cube of a tesseract [1,2].

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

Page edit log

Victor V. Albert (2024-09-10) — most recent

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.