Suppressing logical errors on an encoded subspace using logical dynamical decoupling. Part I: Theory

It is well known that a quantum code's efficacy is limited by its distance, which determines the smallest weight error which the code cannot detect. Often, to address this issue, the code is exchanged for one with a larger distance. This solution is viable, but ultimately still leaves the code space susceptible to certain high-weight errors. In this talk, we present a new method for dealing with these higher-weight errors, logical dynamical decoupling (LDD) , which works symbiotically with the existing quantum code infrastructure for any stabilizer code. Using LDD, we are able to correct or suppress all errors up to weight n which can affect an [[n, k, d]] stabilizer code.