Tower of Structured Excited States from Measurements

Preparing highly entangled quantum states on quantum platforms remains a central challenge in quantum information science and condensed matter physics. While previous studies have primarily focused on measurement-based preparation using local observables, we introduce a novel approach that leverages global observables to efficiently generate entanglement across an entire quantum system. Specifically, our log-depth protocol employs quantum phase estimation to measure global observables such as total magnetization and momentum through local measurements, enabling the preparation of structured excited states from area-law entangled states. This method facilitates the preparation of quantum many-body scar states in diverse models, including the Affleck-Kennedy-Lieb-Tasaki model, constrained domain-wall models, and spin-1/2 and spin-1 XX chains, and it is also applicable for generating high-weight Dicke states. Moreover, our nondestructive momentum measurement enables the preparation of states such as the Arovas A state. By integrating theoretical insights with experimental feasibility-where all operations involve only few-bit gates and limited postselection-we propose measurement-based approaches as powerful tools for accessing highly excited states, with applications in quantum metrology, error correction, and the study of nonequilibrium quantum dynamics.