Absorbing Phases in Adaptive Circuits

I will discuss the construction of specific target states in 1D quantum circuits using measurements followed by outcome-dependent feedback. There is a critical rate of measurement above which these protocols can be successful, but symmetries can impact their viability. By studying two families of models - qubits undergoing unitary evolution with a special structure, and free fermions - a Z2 symmetry is found to slow the preparation of such states. This is explained by a mapping to Branching-Annihilating Random Walks.