Unitary code[1]
Description
Encodes \(K\) states (codewords) into the unitary group \(U(N)\), with codewords represented by matrices.Cousin
- Orthogonal Spacetime Block Code (OSTBC)— Orthogonal spacetime block codes with complex coefficients for \(T=n\) are unitary codes.
Member of code lists
Primary Hierarchy
Parents
The unitary group is a compact symmetric space \(G/H\) with \(G=U(N)\times U(N)\) and \(H = U(N)\) [3; Table 3].
Unitary code
Children
Codewords of the Alamouti code are two-dimensional unitary matrices.
Unitary \(t\)-designs are designs on the unitary group \(U(N)\). Random \(n\)-qubit unitary circuits form approximate unitary designs on \(U(2^n)\) at a depth logarithmic in \(n\) [4].
References
- [1]
- A. Roy and A. J. Scott, “Unitary designs and codes”, Designs, Codes and Cryptography 53, 13 (2009) arXiv:0809.3813 DOI
- [2]
- J. Creignou and H. Diet, “Linear programming bounds for unitary space time codes”, (2008) arXiv:0803.1227
- [3]
- C. Bachoc, D. C. Gijswijt, A. Schrijver, and F. Vallentin, “Invariant Semidefinite Programs”, International Series in Operations Research & Management Science 219 (2011) arXiv:1007.2905 DOI
- [4]
- T. Schuster, J. Haferkamp, and H.-Y. Huang, “Random unitaries in extremely low depth”, (2025) arXiv:2407.07754
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2025-10-27)
Cite as:
“Unitary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/unitary, arXiv:2606.11484