  Long-range entangled quantum states -- like cat states and topological order
-- are key for quantum metrology and information purposes, but they cannot be
prepared by any scalable unitary process. Intriguingly, using measurements as
an additional ingredient could circumvent such no-go theorems. However,
efficient schemes are known for only a limited class of long-range entangled
states, and their implementation on existing quantum devices via a sequence of
gates and measurements is hampered by high overheads. Here we resolve these
problems, proposing how to scalably prepare a broad range of long-range
entangled states with the use of existing experimental platforms. Our two-step
process finds an ideal implementation in Rydberg atom arrays, only requiring
time-evolution under the intrinsic atomic interactions, followed by measuring a
single sublattice (by using, e.g., two atom species). Remarkably, this protocol
can prepare the 1D Greenberger-Horne-Zeilinger (GHZ) 'cat' state and 2D toric
code with fidelity per site exceeding $0.9999$, and a 3D fracton state with
fidelity $\gtrapprox 0.998$. In light of recent experiments showcasing 3D
Rydberg atom arrays, this paves the way to the first experimental realization
of fracton order. While the above examples are based on efficiently preparing
and measuring cluster states, we also propose a multi-step procedure to create
$S_3$ and $D_4$ non-Abelian topological order in Rydberg atom arrays and other
quantum devices -- offering a route towards universal topological quantum
computation.
