  We develop a model for quantum computation with Rydberg atom arrays, which
only relies on global driving, without the need of local addressing of the
qubits: any circuit is executed by a sequence of global, resonant laser pulses
on a static atomic arrangement. We present two constructions: for the first,
the circuit is imprinted in the trap positions of the atoms and executed by the
pulses; for the second, the atom arrangement is circuit-independent, and the
algorithm is entirely encoded in the global driving sequence. Our results show
in particular that a quadratic overhead in atom number is sufficient to
eliminate the need for local control to realize a universal quantum processor.
We give explicit protocols for all steps of an arbitrary quantum computation,
and discuss strategies for error suppression specific to our model. Our scheme
is based on dual-species processors with atoms subjected to Rydberg blockade
constraints, but it might be transposed to other setups as well.
