  Quantum entanglement involving coherent superpositions of macroscopically
distinct states is among the most striking features of quantum theory, but its
realization is challenging, since such states are extremely fragile. Using a
programmable quantum simulator based on neutral atom arrays with interactions
mediated by Rydberg states, we demonstrate the deterministic generation of
'Schr\"odinger cat' states of the Greenberger-Horne-Zeilinger (GHZ) type with
up to 20 qubits. Our approach is based on engineering the energy spectrum and
using optimal control of the many-body system. We further demonstrate
entanglement manipulation by using GHZ states to distribute entanglement to
distant sites in the array, establishing important ingredients for quantum
information processing and quantum metrology.
