Gnu code: Difference between revisions

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Revision as of 08:45, 9 May 2021

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In [[quantum information]], the '''gnu code''' refers to a particular family of [[quantum error correction|quantum error correcting codes]], with the special property of being invariant under [[permutations]] of the qubits. Given integers ''g'' (the ''gap''), ''n'' (the occupancy), and ''m'' (the length of the code), the two codewords are

:<math>|0_L0_{\rm L}\rangle = \sum_{\ell\, \textrm{even}\atop 0\le\ell\le n} \sqrt{\frac{{n\choose \ell}}{2^{n-1}}} |D^m_{g\ell}\rangle</math>

:<math>|1_L1_{\rm L}\rangle = \sum_{\ell\, \textrm{odd}\atop 0\le\ell\le n} \sqrt{\frac{{n\choose \ell}}{2^{n-1}}} |D^m_{g\ell}\rangle</math>

where <math>|D^m_k\rangle</math> are the [[Dicke states]] consisting of a uniform superposition of all weight-''k'' words on ''m'' qubits, e.g.