Measurement as a Shortcut to Long-Range Entangled Quantum Matter

The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes local adaptive that enable low-depth quantum matter characterized gapped topological orders conformal field theories (CFTs). are inspired distinct physical insights, including tensor-network constructions, multiscale entanglement renormalization ansatz (MERA), parton constructions. A large class orders, chiral order, be prepared in constant depth or time, one-dimensional CFT non-abelian both solvable non-solvable groups scaling logarithmically system size. also build on a recently discovered correspondence between symmetry-protected phases to derive efficient protocols for preparing symmetry-enriched order arbitrary CSS (Calderbank-Shor-Steane) codes. Our work illustrates the practical conceptual versatility measurement state preparation.