Bad Qubits — Learn Quantum by Doing

Multiple choice

Shor's nine-qubit

[[9,1,3]]

code concatenates the phase-flip and bit-flip repetition codes and has

n - k = 8

independent stabilizer generators. How are these 8 generators split between

Z

-type and

X

-type checks?

Four $Z$ -type and four $X$ -type generators, evenly split across all nine qubits
Two $Z$ -type generators checking bit parities between blocks, plus six $X$ -type generators checking phase parities within blocks
Eight $Z$ -type generators only; the $X$ errors are handled without any stabilizer checks
Six $Z$ -type generators ( $Z_1Z_2, Z_2Z_3, Z_4Z_5, Z_5Z_6, Z_7Z_8, Z_8Z_9$ ) checking bit parities within each block of three, plus two $X$ -type generators ( $X_1..X_6, X_4..X_9$ ) checking phase parities between blocks