[Jump to code hierarchy]

\([[8,1,2]]\) CSS code[1]

Description

A stabilizer code that admits a logical \(T\) gate via application of physical \(T\) gates and a \(CZ\)-like gate.

Transversal Gates

Logical \(T\) gate via application of physical \(T\) gates and a \(CZ\)-like gate [1].

Cousins

  • \([[15,1,3]]\) quantum RM code— The \([[8,1,2]]\) code can be obtained by contracting some of the legs of the \([[15,1,3]]\) encoding map and concatenating one leg with a repetition code [2].
  • Tensor-network code— The \([[8,1,2]]\) code can be obtained by contracting some of the legs of the \([[15,1,3]]\) encoding map and concatenating one leg with a repetition code [2].

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 Hamiltonian-based QECC Quantum
Parents
Qubit CSS code
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[8,1,2]]\) CSS code

References

[1]
R. Shen, Y. Wang, and C. Cao, “Quantum Lego and XP Stabilizer Codes”, Quantum 9, 1876 (2025) arXiv:2310.19538 DOI
[2]
M. Vasmer and A. Kubica, “Morphing Quantum Codes”, PRX Quantum 3, (2022) arXiv:2112.01446 DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: stab_8_1_2

Cite as:
“\([[8,1,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/stab_8_1_2
BibTeX:
@incollection{eczoo_stab_8_1_2, title={\([[8,1,2]]\) CSS code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_8_1_2} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/stab_8_1_2

Cite as:

“\([[8,1,2]]\) CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/stab_8_1_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/8/stab_8_1_2.yml.