Description
Member of CSS code family constructed with a first-order punctured RM\((1,r)\) \([2^r-1,r+1,2^{r-1}-1]\) code and its even subcode for \(r \geq 3\). Each code transversally implements a member of an infinite family of diagonal gates from the Clifford hierarchy [3].
Transversal Gates
\(Z\)-rotation by angle \(-\pi/2^{r-1}\) [2]. These are the smallest qubit stabilizer codes with such a gate [4].
Parents
Children
References
- [1]
- D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations”, Nature 402, 390 (1999) arXiv:quant-ph/9908010 DOI
- [2]
- B. Zeng et al., “Local unitary versus local Clifford equivalence of stabilizer and graph states”, Physical Review A 75, (2007) arXiv:quant-ph/0611214 DOI
- [3]
- S. X. Cui, D. Gottesman, and A. Krishna, “Diagonal gates in the Clifford hierarchy”, Physical Review A 95, (2017) arXiv:1608.06596 DOI
- [4]
- S. Koutsioumpas, D. Banfield, and A. Kay, “The Smallest Code with Transversal T”, (2022) arXiv:2210.14066
Page edit log
- Victor V. Albert (2022-11-15) — most recent
Cite as:
“\([[2^r-1, 1, 3]]\) quantum Reed-Muller code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/diagonal_clifford