Classical Optimization Strategies for Variational Quantum Algorithms: A Systematic Study of Noise Effects and Parameter Efficiency

TL;DR

This paper systematically evaluates classical optimization methods for Variational Quantum Algorithms under noise, revealing that focusing on active parameters improves efficiency and robustness in near-term quantum devices.

Contribution

It introduces a parameter-filtered optimization approach based on landscape analysis, enhancing efficiency and noise resilience for VQAs.

Findings

Filtering active parameters reduces optimization evaluations.

Parameter filtering improves robustness against noise.

Structural insights aid in noise mitigation strategies.

Abstract

This study systematically benchmarks classical optimization strategies for the Quantum Approximate Optimization Algorithm when applied to Generalized Mean-Variance Problems under near-term Noisy Intermediate-Scale Quantum conditions. We evaluate Dual Annealing, Constrained Optimization by Linear Approximation, and the Powell Method across noiseless, sampling noise, and two thermal noise models. Our Cost Function Landscape Analysis revealed that the Quantum Approximate Optimization Algorithm angle parameters $\gamma$ were largely inactive in the noiseless regime. This insight motivated a parameter-filtered optimization approach, in which we focused the search space exclusively on the active $\beta$ parameters. This filtering substantially improved parameter efficiency for fast optimizers like Constrained Optimization by Linear Approximation (reducing evaluations from 21 to 12 in the noiseless case) and enhanced robustness, demonstrating that leveraging structural insights is an effective architecture-aware noise mitigation strategy for Variational Quantum Algorithms.