Absorbing State Phase Transitions and Stability of Long-Range Coherence in Dissipative Quantum State Preparation

We introduce a purely dissipative quantum state preparation procedure for a variety of long-range coherent states, including a vortex lattice. We show how errors—even when they preserve the target state as a dark state—may ruin dissipative state preparation by inducing a phase transition towards a mixed state. We find a tradeoff between all-to-all (where preparation takes finite time, but is fragile to errors) and local procedures (where preparation time grows with system size, but is robust to errors). The model is also of interest as a quantum reaction-diffusion model where the absorbing state itself has long-range coherence.