Entanglement is an essential concept in quantum mechanics and governs many modern areas of research in physics. The emergence of entanglement is typically associated with the application of unitaries coupling multiple particles. This scrambling is counteracted by the inherent instability of entanglement under monitoring, as local measurements tend to disentangle systems. This thesis studies locally connected random quantum circuits in one dimension, which have proven to be a useful platform for the investigation of entanglement phenomena out of equilibrium. In particular, the competition of different kinds of unitary gates and measurements can drive transitions between distinct entangling phases. We investigate such quantum circuits with focus on extended regimes that follow critical scaling laws. We further examine the capabilities of a specific quantum circuit model (the projective transverse field Ising model) as a quantum error correcting code. Our findings motivate an approach to make the entanglement transition of this model experimentally accessible.
