🤖 AI Summary
Addressing the three key challenges in parameterized quantum circuit optimization—non-convex objective landscapes, high gradient noise, and barren plateaus—this work systematically evaluates natural gradient and second-order optimizers for QAOA-based MaxCut solving. We propose SP-BFGS: a robust quasi-Newton method that integrates secant penalty regularization into the BFGS framework to enhance resilience against gradient noise while preserving convergence stability and computational efficiency. SP-BFGS combines quantum natural gradient estimation, BFGS-type Hessian approximation, secant-constrained regularization, and shallow-depth QAOA simulation. On synthetic MaxCut instances, SP-BFGS achieves significantly faster convergence and higher-quality solutions compared to standard BFGS and Adam, demonstrating its effectiveness and practicality for noisy intermediate-scale quantum (NISQ) optimization.
📝 Abstract
The optimization of parametric quantum circuits is technically hindered by three major obstacles: the non-convex nature of the objective function, noisy gradient evaluations, and the presence of barren plateaus. As a result, the selection of classical optimizer becomes a critical factor in assessing and exploiting quantum-classical applications. One promising approach to tackle these challenges involves incorporating curvature information into the parameter update. The most prominent methods in this field are quasi-Newton and quantum natural gradient methods, which can facilitate faster convergence compared to first-order approaches. Second order methods however exhibit a significant trade-off between computational cost and accuracy, as well as heightened sensitivity to noise. This study evaluates the performance of three families of optimizers on synthetically generated MaxCut problems on a shallow QAOA algorithm. To address noise sensitivity and iteration cost, we demonstrate that incorporating secant-penalization in the BFGS update rule (SP-BFGS) yields improved outcomes for QAOA optimization problems, introducing a novel approach to stabilizing BFGS updates against gradient noise.