2
$\begingroup$

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?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

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

Improve this answer
$\endgroup$
2
  • $\begingroup$ Do you know if this $ ((11,2,5)) $ CWS code is equivalent to a stabilizer code? $\endgroup$
    – Ian Gershon Teixeira
    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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.