Probing entanglement and parameter sensitivity in QAOA via Quantum Fisher Information
Brian García Sarmina, Jorge Saavedra Benavides, Guo-Hua Sun, Shi‐Hai Dong · Quantum Review Letters · 2025
Variational Quantum Algorithms (VQAs) are leading candidates for achieving near-term quantum advantage, yet important questions remain regarding parameter relevance and the role of entanglement in shaping their behavior. In this work, we employ the Quantum Fisher Information (QFI) as a diagnostic tool to quantify the sensitivity and correlations of QAOA states with respect to parameter variations. We study Max-Cut on cyclic and complete graphs, as well as random Ising model (RIM) instances, comparing RX-only and hybrid RX-RY mixers up to depth ( ) with optional entanglement stages and patterns. Across problem classes, complete-graph Max-Cut instances generate substantially larger QFI eigenvalues and covariance fractions than cyclic ones, exceeding the shot-noise scaling ( ) while remaining below the Heisenberg limit ( ). Entanglement primarily amplifies cross-parameter correlations, and its benefits saturate rapidly: the first entangling stage produces the dominant increase in QFI, while additional stages often yield diminishing or even adverse returns. A key methodological contribution of this work is the use of averaged QFI matrices over random parameter samples, which exposes robust global trends and reveals strongly non-uniform parameter relevance across architectures and depths. Leveraging these insights, we propose a QFI-Informed Mutation (QIm) heuristic that adapts mutation probabilities and step sizes using diagonal QFI entries. QIm improves convergence and stability over uniform and random-restart baselines, especially at large depths and in RIM landscapes. In general, our results position QFI as both a structural probe of QAOA ansätze and a practical resource to guide the design of effective optimization strategies in the NISQ regime.