Quantum chaos and circuit parameter optimization

Joonho Kim, Yaron Oz*, Dario Rosa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Article number023104
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number2
StatePublished - 1 Feb 2023


  • circuit optimization
  • quantum chaos
  • variational algorithms


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