Sculpting Long-Range Entanglement with Adaptive Circuits: From Theory to Realizing Non-Abelian Anyons and Nishimori Transitions

Long-range entangled states of matter exhibit rich and powerful properties but cannot be prepared in constant depth using local unitary protocols. Remarkably, the wave-function collapse induced by quantum measurements can bypass no-go theorems, thereby efficiently preparing such states. In this talk, we will explore recent advances in this direction, which can now be implemented in programmable quantum devices. For instance, measuring on Quantinuum's trapped-ion processor has made it possible to create non-Abelian topological order, including control of its non-Abelian anyons. Moreover, the stability of such measurement-based protocols has been explored on IBM's superconducting qubit chip, leading to the sighting of a Nishimori transition at the error threshold. More generally, we will review the current state of the art and discuss future possibilities.