Quantum Chaos and Circuit Parameter Optimization

TL;DR

This paper investigates quantum chaos indicators in variational quantum circuits, analyzing their relation to circuit expressibility and optimization, and compares different random matrix models to improve understanding of circuit performance.

Contribution

It introduces a novel analysis of quantum chaos diagnostics in variational circuits, linking operator spreading and eigenvalue spectra to circuit expressibility and optimization.

Findings

Universal structure of random matrix models in high-depth circuits

Different layer unitaries impact VQA performance

Potential tension between OTOC and BGS diagnostics of chaos

Abstract

We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the universal structure of random matrix models in high-depth circuit states. We construct different layer unitaries corresponding to the GOE and GUE distributions and quantify their VQA performance. Our study also highlights a potential tension between the OTOC and BGS-type diagnostics of quantum chaos.