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

TL;DR

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 to demonstrate that leveraging structural insights is an effective architecture-aware noise mitigation strategy for Variational Quantum Algorithms.

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 $γ$ 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 $β$ 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.

Figures (5)

• Figure 1: Full qaoa optimization landscapes (noiseless State Vector simulation) showing pairwise parameter dependencies. Other parameters are fixed at the global minimum (red point).
• Figure 2: Full qaoa optimization landscapes (Sampling Noise simulation, 1024 shots) showing pairwise parameter dependencies. Other parameters are fixed at the global minimum (red point).
• Figure 3: Full qaoa optimization landscapes (Thermal Noise-A: $T_1 = 380\mu s, T_2 = 400 \mu s$, 1024 shots) showing pairwise parameter dependencies. Other parameters are fixed at the global minimum (red point).
• Figure 4: Full qaoa optimization landscapes (Thermal Noise-A: $T_1 = 80\mu s, T_2 = 100 \mu s$, 1024 shots) showing pairwise parameter dependencies. Other parameters are fixed at the global minimum (red point).
• Figure 5: Combined qaoa Convergence Benchmark of Classical Optimizers under four noise profiles (Sec. \ref{['sec:noise_profiles']}). (a) shows results from the standard optimization approach, and (b) shows the results from the parameter-filtered approach. Blue dots show 10 individual runs (Primary Y-axis: Function Value). Red markers and error bars show the mean and $95\%$ confidence interval. Gray bars (Secondary Y-axis) indicate the average number of function evaluations.