  We consider information spreading measures in randomly initialized
variational quantum circuits and introduce entanglement diagnostics for
efficient variational quantum/classical computations. We establish a robust
connection between entanglement measures and optimization accuracy by solving
two eigensolver problems for Ising Hamiltonians with nearest-neighbor and
long-range spin interactions. As the circuit depth affects the average
entanglement of random circuit states, the entanglement diagnostics can
identify a high-performing depth range for optimization tasks encoded in local
Hamiltonians. We argue, based on an eigensolver problem for the
Sachdev-Ye-Kitaev model, that entanglement alone is insufficient as a
diagnostic to the approximation of volume-law entangled target states and that
a large number of circuit parameters is needed for such an optimization task.
