Description
Smallest 3D color code whose physical qubits lie on vertices of a cube and which admits a transversal CCZ gate. Similar constructions exist on \(d\)-dimensional hypercubes and are called hyperoctahedron \([[2^d,d,2]]\) codes [3].
Transversal Gates
Fault Tolerance
CCZ gate can be distilled in a fault-tolerant manner [5].
Parents
- Color code — The \([[8,3,2]]\) code is the smallest non-trivial 3D color code.
- Small-distance block quantum code
Cousins
- \([[15,1,3]]\) quantum Reed-Muller code — The \([[8,3,2]]\) code can be obtained from a subset of physical qubits of the \([[15,1,3]]\) code [3].
- \([[4,2,2]]\) CSS code — The \([[4,2,2]]\) (\([[8,3,2]]\)) code's physical qubits correspond to vertices of a square (cube). Similar constructions exist on \(d\)-dimensional hypercubes and are called hyperoctahedron \([[2^d,d,2]]\) codes [3].
References
- [1]
- A. Kubica, B. Yoshida, and F. Pastawski, “Unfolding the color code”, New Journal of Physics 17, 083026 (2015) arXiv:1503.02065 DOI
- [2]
- 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.
- [3]
- M. Vasmer and A. Kubica, “Morphing Quantum Codes”, PRX Quantum 3, (2022) arXiv:2112.01446 DOI
- [4]
- 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
- [5]
- J. Haah and M. B. Hastings, “Measurement sequences for magic state distillation”, Quantum 5, 383 (2021) arXiv:2007.07929 DOI
Page edit log
- Victor V. Albert (2022-12-03) — most recent
Cite as:
“\([[8,3,2]]\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/stab_8_3_2