Efficient computations of encodings for quantum error correction
Richard Cleve, Daniel Gottesman · Physical Review A · 1997
We show how, given any set of generators of the stabilizer of a quantum code, an efficient gate array that computes the code words can be explicitly constructed. For an $n$-qubit code whose stabilizer has $d$ generators, the resulting gate array consists of $O(\mathrm{nd})$ operations, and converts $k$-qubit data (where $k=n\ensuremath{-}d)$ into $n$-qubit code words.