  Measurement-based quantum computation, an alternative paradigm for quantum
information processing, uses simple measurements on qubits prepared in cluster
states, a class of multiparty entangled states with useful properties. Here we
propose and analyze a scheme that takes advantage of the interplay between
spin-orbit coupling and superexchange interactions, in the presence of a
coherent drive, to deterministically generate macroscopic arrays of cluster
states in fermionic alkaline earth atoms trapped in three dimensional (3D)
optical lattices. The scheme dynamically generates cluster states without the
need of engineered transport, and is robust in the presence of holes, a typical
imperfection in cold atom Mott insulators. The protocol is of particular
relevance for the new generation of 3D optical lattice clocks with coherence
times $>10$ s, two orders of magnitude larger than the cluster state generation
time. We propose the use of collective measurements and time-reversal of the
Hamiltonian to benchmark the underlying Ising model dynamics and the generated
many-body correlations.
