Shor's quantum 9 bit code

Question

Regarding Shor's quantum 9 bit error correction code, is the code corrects any error on any single qbit? Or is it corrects only a phase or a bit flip? How can i verify that?

Answer 1

Shor's 9-qubit code can correct against any single qubit error, as is explained e.g. in these lecture notes. You can verify this by e.g. checking the quantum error correction condition for the two codewords.