Rewiring Stabilizer Codes

We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and corrected in part by repeatedly measuring redundant degrees of freedom. We show how to construct a set of projective measurements which will map between two arbitrary stabilizer codes. We show that this process preserves all quantum information. It can be used to implement Clifford gates, braid extrinsic defects, or move between codes in which different operations are natural.