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Citation bot (talk | contribs) Add: eprint, class. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Abductive | Category:Quantum information science | #UCB_Category 147/171 |
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{{DISPLAYTITLE:''gnu'' code}}
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
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:<math>|D^4_2\rangle = \frac{|0011\rangle + |0101\rangle + |1001\rangle + |0110\rangle + |1010\rangle + |1100\rangle}{\sqrt{6}}</math>
The real parameter <math>u = \frac{m}{gn}</math> scales the density of the code. The length <math>m = gnu</math>, hence the name of the code. For odd <math>g = n</math> and <math>u \ge 1</math>, the ''gnu'' code is capable of correcting <math>\frac{g-1}{2}</math> [[erasure error]]s,<ref name="Ouyang p. ">{{cite journal | last=Ouyang | first=Yingkai | title=Permutation-invariant quantum codes | journal=Physical Review A
==References==
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