Smolin-Smith-Wehner (SSW) code[1,2] 

Description

A family of \(((n=4k+2l+3,M_{k,l},2))\) CWS codes, where \(M_{k,l} \approx 2^{n-2}(1-\sqrt{2/(\pi(n-1))})\), whose codewords are superpositions of particular bitstrings and their complements. For \(n \geq 11\), these codes have a logical subspace whose dimension is larger than that of the largest stabilizer code for the same \(n\) and \(d\). A subset of these codes can be augmented to yield codes with one higher logical dimension [3].

Parents

Cousins

References

[1]
J. A. Smolin, G. Smith, and S. Wehner, “Simple Family of Nonadditive Quantum Codes”, Physical Review Letters 99, (2007) arXiv:quant-ph/0701065 DOI
[2]
K. Feng and C. Xing, “A new construction of quantum error-correcting codes”, Transactions of the American Mathematical Society 360, 2007 (2007) DOI
[3]
S. Yu, Q. Chen, and C. H. Oh, “Graphical Quantum Error-Correcting Codes”, (2007) arXiv:0709.1780
[4]
A. Cross et al., “Codeword Stabilized Quantum Codes”, IEEE Transactions on Information Theory 55, 433 (2009) arXiv:0708.1021 DOI
[5]
Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: ssw

Cite as:
“Smolin-Smith-Wehner (SSW) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ssw
BibTeX:
@incollection{eczoo_ssw, title={Smolin-Smith-Wehner (SSW) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/ssw} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/ssw

Cite as:

“Smolin-Smith-Wehner (SSW) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ssw

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/ssw.yml.