Infinite-randomness criticality in monitored quantum dynamics with static disorder

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random circuits spatially varying measurement rates. These undergo measurement-induced phase transition (MIPT) in their entanglement structure, but the nature critical point differs drastically from case constant rate. In particular, at rate, we find that subsystem size $\ell$ scales as $S \sim \sqrt{\ell}$; moreover, dynamical exponent $z = \infty$. The MIPT is flanked by Griffiths phases continuously exponents. argue for this infinite-randomness scenario on general grounds and present numerical evidence it captures some features universal properties using large-scale simulations Clifford circuits. findings demonstrate relevance irrelevance perturbations to can naturally be interpreted powerful heuristic known Harris criterion.