Abstract: The stochastic, non-unitary nature of measurement is a cornerstone of quantum theory and stands in stark contrast with the deterministic, unitary evolution prescribed by Schrodinger’s equation. Due to these unique properties, measurement is key to fundamental protocols in quantum information science such as teleportation, error correction and measurement-based computation. All these protocols use quantum measurements, and classical processing of their outcomes, to build particular structures of quantum information in space-time. I will present some results [1] on these “monitored” circuits comprising both unitary gates and controlled projective measurements. Time permitting, I will also discuss another work [2], which experimentally realized quasiparticles with non-Abelinian exchange statistics, a key ingredient in topological quantum computing. [1] Hoke et al., Nature 622, 481–486 (2023) [2] Andersen et al., Nature 618, 264–269 (2023)