Fault-tolerant switching between generic stabilizer codes. (arXiv:1709.09282v3 [quant-ph] UPDATED)
We propose a randomized variant of the stabilizer rewiring algorithm (SRA), a
method for constructing a transversal circuit mapping between any pair of
stabilizer codes. As gates along this circuit are applied, the initial code is
deformed through a series of intermediate codes before reaching the final code.
The circuit is then fault-tolerant if the full set of intermediate codes have
high distance. With this randomized variant, we show that there always exists a
path of deformations which preserves the code distance throughout the circuit,
while using at most linear overhead in the distance. Furthermore, we show that
a random path will almost always suffice. This allows constructive, low
overhead fault-tolerant code switching between generic stabilizer
error-correcting codes. As proof of principle, we use this variant to construct
a particular fault-tolerant conversion circuit that is more space efficient
than previously known solutions.