A CWS code can be defined in terms of stabilizer codes/stabilizer states and graph states. See What is an example of a non-additive code that is not a CWS code?

Is the $ ((11,2,3)) $ nonadditive quantum error-correcting code given in On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes a codeword stabilized code?

Certainly all the coefficients are $ \pm 1 $ up to a global scalar (in fact all the nonzero coefficients are $ +1 $) so that necessary condition is met.

Maybe there is some way of confirming this (or deriving a contradiction) by think about what graph that $ ((11,2,3)) $ code would have to correspond to?


1 Answer 1


There exists a CWS code with parameters ((11,2,5)) with a graph specified in 1, p. 89.

  • $\begingroup$ Do you know if this $ ((11,2,5)) $ CWS code is equivalent to a stabilizer code? $\endgroup$ Aug 8 at 18:11
  • $\begingroup$ Sorry, I do not know. In general, CWS codes can have better parameters than stabilizer codes, e.g., there is a ((9,12,3)) and a ((10,24,3)) code outperforming the stabilizer codes with the same number of qubits. $\endgroup$
    – Creeper
    Aug 25 at 8:07

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