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Long-range entangled quantum states -- like cat states and topological order-- are key for quantum metrology and information purposes, but they cannot beprepared by any scalable unitary process. Intriguingly, using measurements asan additional ingredient could circumvent such no-go theorems. However,efficient schemes are known for only a limited class of long-range entangledstates, and their implementation on existing quantum devices via a sequence ofgates and measurements is hampered by high overheads. Here we resolve theseproblems, proposing how to scalably prepare a broad range of long-rangeentangled states with the use of existing experimental platforms. Our two-stepprocess finds an ideal implementation in Rydberg atom arrays, only requiringtime-evolution under the intrinsic atomic interactions, followed by measuring asingle sublattice (by using, e.g., two atom species). Remarkably, this protocolcan prepare the 1D Greenberger-Horne-Zeilinger (GHZ) 'cat' state and 2D toriccode with fidelity per site exceeding $0.9999$, and a 3D fracton state withfidelity $\gtrapprox 0.998$. In light of recent experiments showcasing 3DRydberg atom arrays, this paves the way to the first experimental realizationof fracton order. While the above examples are based on efficiently preparingand 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 otherquantum devices -- offering a route towards universal topological quantumcomputation.

Efficiently preparing Schr\"odinger's cat, fractons and non-Abelian topological order in quantum devices