The goal of building a quantum computer has lead to rapid advances in experiments that allow for high-precision dynamical control of quantum systems at the single qubit level. However, a major challenge in harnessing the power of these devices is in understanding how best to control noise. In particular, many interesting phases of matter, including topological phases, that exist in closed quantum systems are not stable at finite temperature, suggesting that they are particularly sensitive to the kinds of open-system noise present in such devices. Quantum error correction protocols can be used to rectify this, but these involve non-local processes. In this talk, I will explore approaches to stabilizing symmetry-protected topological order at arbitrarily long times in 1 dimension using local open-system dynamics. I will show that this can be done when the noise is of a particular type relevant to Rydberg atom arrays, known as biased erasure noise, and comment on the implications of these results for possible steady-state phases of open quantum systems.
