  We consider information spreading measures in randomly initialized
variational quantum circuits and construct entanglement diagnostics for
efficient quantum/classical hybrid computations. Following the Renyi entropies
of the random circuit's reduced density matrix, we divide the number of circuit
layers into two separate regions with a transitioning zone between them. We
identify the high-performance region for solving optimization problems encoded
in the cost function of k-local Hamiltonians. We consider three example
Hamiltonians, i.e., the nearest-neighbor transverse-field Ising model, the
long-range transverse-field Ising model and the Sachdev-Ye-Kitaev model. By
analyzing the qualitative and quantitative differences in the respective
optimization processes, we demonstrate that the entanglement measures are
robust diagnostics that are highly correlated with the optimization
performance. We study the advantage of entanglement diagnostics for different
circuit architectures and the impact of changing the parameter space
dimensionality while maintaining its entanglement structure.
