MITIGATING COHERENT NOISE

https://dukespace.lib.duke.edu/items/ffc1b55d-d946-4b6c-8415-97bfbf1cf4ca Stochastic errors in quantum systems occur randomly but coherent errors may be more damaging since they can accumulate in a particular direction. We develop a framework for designing decoherence free subspaces (DFS), that are unperturbed by coherent noise. We consider a particular form of coherent $Z$-errors and construct stabilizer codes that form DFS for such noise (``Z-DFS''). More precisely, we develop conditions for transversal $\exp(\imath \theta \sigma_Z)$ to preserve a stabilizer code subspace for all $\theta$. If the code is error-detecting, then this implies a trivial action on the logical qubits. These conditions require the existence of a large number of weight-$2$ $Z$-stabilizers, and together, these weight-$2$ $Z$-stabilizers generate a direct product of single-parity-check codes.