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Subset-Sum-Linear-Programming (SS-LP) code[1]

Description

Qubit block quantum code that encodes a logical qubit and that is constructed using the Subset-Sum-Linear-Programming (SS-LP) numerical construction. SS-LP codes are optimized to admit diagonal gates transversally and include \(((7,2,3))\) codes that realize the \(\mathsf{BD}_{16}\) and \(\mathsf{BD}_{32}\) groups transversally, yielding \(T\) and \(\sqrt{T}\) gates, respectively. Larger codes include an \(((8,2,3))\) code that transversally realizes \(\mathsf{BD}_{64}\).

Transversal Gates

SS-LP codes are optimized to admit diagonal gates transversally and include \(((7,2,3))\) codes that realize the \(\mathsf{BD}_{16}\) and \(\mathsf{BD}_{32}\) groups transversally, yielding \(T\) and \(\sqrt{T}\) gates, respectively. Larger codes include an \(((8,2,3))\) code that transversally realizes \(\mathsf{BD}_{64}\).

Cousins

  • \([[15,1,3]]\) quantum Reed-Muller code— The \(((7,2,3))\) SS-LP code realizes the \(T\) gate transversally, but requires fewer qubits than the \([[15,1,3]]\) quantum Reed-Muller code.
  • Binary dihedral PI code— SS-LP codes are optimized to admit diagonal gates transversally and include \(((7,2,3))\) codes that realize the \(\mathsf{BD}_{16}\) and \(\mathsf{BD}_{32}\) groups transversally, yielding \(T\) and \(\sqrt{T}\) gates, respectively. Larger codes include an \(((8,2,3))\) code that transversally realizes \(\mathsf{BD}_{64}\).

Primary Hierarchy

References

[1]
C. Zhang, Z. Wu, S. Huang, and B. Zeng, “Transversal Gates in Nonadditive Quantum Codes”, (2025) arXiv:2504.20847
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Zoo Code ID: sslp

Cite as:
“Subset-Sum-Linear-Programming (SS-LP) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/sslp
BibTeX:
@incollection{eczoo_sslp, title={Subset-Sum-Linear-Programming (SS-LP) code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/sslp} }
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Permanent link:
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Cite as:

“Subset-Sum-Linear-Programming (SS-LP) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/sslp

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/sslp.yml.