Quantum chaos and circuit parameter optimization

Abstract We consider quantum chaos diagnostics of the variational circuit states at random parameters and explore their connection to expressibility optimizability. By measuring operator spreading coefficient eigenvalue spectrum modular Hamiltonian reduced density matrix, we identify emergence universal matrix ensembles in high-depth states. The that use spectrum, e.g. entanglement entropy, turn out be more accurate measures algorithm optimization efficiency than those level spacing distribution such as r -statistics or spectral form factors.