Prime-qudit RM code[1,2] 

Description

Modular-qudit stabilizer code constructed from generalized Reed-Muller (GRM) codes or their duals via the modular-qudit CSS construction. An odd-prime-qudit CSS code family constructed from first-order punctured RM codes transversally implements a diagonal gate at any level of the qudit Clifford hierarchy [2].

Magic

An odd-prime-qudit CSS code family constructed from first-order punctured RM codes can be used for qudit magic-state distillation; see [2; Table I] for yields.

Transversal Gates

An odd-prime-qudit CSS code family constructed from first-order punctured RM codes transversally implements a diagonal gate at any level of the qudit Clifford hierarchy [2].

Parents

Children

References

[1]
P. K. Sarvepalli and A. Klappenecker, “Nonbinary Quantum Reed-Muller Codes”, (2005) arXiv:quant-ph/0502001
[2]
E. T. Campbell, H. Anwar, and D. E. Browne, “Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes”, Physical Review X 2, (2012) arXiv:1205.3104 DOI
[3]
M. A. Tsfasman and S. G. Vlăduţ, Algebraic-Geometric Codes (Springer Netherlands, 1991) DOI
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Zoo Code ID: qudit_reed_muller

Cite as:
“Prime-qudit RM code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_reed_muller
BibTeX:
@incollection{eczoo_qudit_reed_muller, title={Prime-qudit RM code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qudit_reed_muller} }
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Cite as:

“Prime-qudit RM code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qudit_reed_muller

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits/stabilizer/ag/qudit_reed_muller.yml.