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 and Permutation-Based 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 RM code— The \(((7,2,3))\) SS-LP code realizes the \(T\) gate transversally, but requires fewer qubits than the \([[15,1,3]]\) quantum RM 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
Parents
Subset-Sum-Linear-Programming (SS-LP) code
References
- [1]
- C. Zhang, Z. Wu, S. Huang, and B. Zeng, “Transversal Gates in Nonadditive Quantum Codes”, (2025) arXiv:2504.20847
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2025-04-30)
Cite as:
“Subset-Sum-Linear-Programming (SS-LP) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/sslp, arXiv:2606.11484