\([[2^{2r-1}-1,1,2^r-1]]\) 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.

Parent

Child

References

[1]
J. Preskill. Lecture notes on Quantum Computation. (1997–2020) URL
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Zoo Code ID: single_qubit_clifford

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
BibTeX:
@incollection{eczoo_single_qubit_clifford, title={\([[2^{2r-1}-1,1,2^r-1]]\) quantum punctured Reed-Muller code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/single_qubit_clifford} }
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https://errorcorrectionzoo.org/c/single_qubit_clifford

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/rm/single_qubit_clifford.yml.