\([[10,1,2]]\) CSS code[1]
Description
Smallest stabilizer code to implement a transversal \(T\) gate.
Transversal Gates
Logical \(T\) gate via application of \(T\), \(T^{\dagger}\), and \(CCZ\) [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
- \([[15,1,3]]\) quantum Reed-Muller code — The \([[10,1,2]]\) code can be obtained by morphing the \([[15,1,3]]\) code [1].
- \([[7,1,3]]\) Steane code — A fault-tolerant universal gate set can be done via code switching between the Steane code and the \([[10,1,2]]\) code [2].
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
Page edit log
- Victor V. Albert (2024-03-28) — most recent
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