Description
A family of \(((n=4k+2l+3,M_{k,l},2))\) self-complementary CWS codes, where \(M_{k,l} \approx 2^{n-2}(1-\sqrt{2/(\pi(n-1))})\). 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 \(d\). Ref. [3] augments a star-graph-based subfamily \(((4n+1,M_n,2))\) by one additional graph-state basis word, yielding \(((4n+1,M_n+1,2))\) codes with \(M_n=2^{4n-1}-\frac{1}{2}\binom{4n}{2n}\). In the CWS description of Ref. [4], the underlying stabilizer state is locally Clifford-equivalent to a GHZ state and its standard-form graph is a star graph.Realizations
The \(((5,5,2))\) SSW code has been realized in an NMR device [5].Cousin
- \(((2m+1,3 \times 2^{2m-3},2))\) Rains code— The SSW code outperforms the Rains codes in terms of code parameters at odd \(n > 11\) [4,6].
Primary Hierarchy
Parents
Smolin-Smith-Wehner (SSW) code
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, G. Smith, J. A. Smolin, and B. Zeng, “Codeword Stabilized Quantum Codes”, IEEE Transactions on Information Theory 55, 433 (2009) arXiv:0708.1021 DOI
- [5]
- J. Zhang, M. Grassl, B. Zeng, and R. Laflamme, “Experimental implementation of a codeword-stabilized quantum code”, Physical Review A 85, (2012) arXiv:1111.5445 DOI
- [6]
- A. W. Cross. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. PhD thesis, Massachusetts Institute of Technology, 2008.
Page edit log
- Victor V. Albert (2026-04-22) — most recent
- Victor V. Albert (2023-11-29)
Cite as:
“Smolin-Smith-Wehner (SSW) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/ssw