\([[2^{2r-1}-1,1,2^r-1]]\) quantum punctured Reed-Muller code[1; Ch. 7]
Description
Member of CSS code family constructed with a punctured self-dual RM \([2^r-1,2^{r-1},\sqrt{2}^{r-1}-1]\) code and its even subcode for \(r \geq 2\).Transversal Gates
All single-qubit Clifford gates.Primary Hierarchy
Generalized homological-product qubit CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Parents
The \([[2^{2r-1}-1,1,2^r-1]]\) quantum punctured Reed-Muller codes are special cases of the \([[\sum_{i=w+1}^m \binom{m}{i}, \sum_{i=0}^{w} \binom{m}{i}, \sum_{i=w+1}^{r+1} \binom{r+1}{i}]]\) family for \(m \to 2r-1\), \(w \to 0\), and \(r \to r-1\).
\([[2^{2r-1}-1,1,2^r-1]]\) quantum punctured Reed-Muller code
Children
References
- [1]
- J. Preskill. Lecture notes on Quantum Computation. (1997–2020) URL
Page edit log
- Victor V. Albert (2022-11-17) — most recent
- Ian Teixeira (2021-11-17)
- Victor V. Albert (2022-11-15)
Cite as:
“\([[2^{2r-1}-1,1,2^r-1]]\) quantum punctured Reed-Muller code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/single_qubit_clifford