Adaptive Rotation for iSOMA: Geometry, Benchmarking, and Noise Robustness in Variational Quantum Objectives

2026-09-29

AI Summary

This study addresses the coordinate-system sensitivity and performance limitations of the iSOMA algorithm in complex geometric and noisy environments by proposing iSOMA-AR. The proposed method constructs an adaptive rotation basis by learning historically successful migration displacements and introduces a selective perturbation mask to eliminate coordinate dependence, while preserving the computationally inexpensive leader-guided migration mechanism of the original algorithm. Experimental evaluations demonstrate that iSOMA-AR significantly outperforms the baseline on the BBOB benchmark, partially surpasses iL-SHADE on CEC test suites, and exhibits high robustness in variational quantum objective optimization. Overall, this work effectively enhances the geometric adaptability and generalization capability of the algorithm.

Abstract

We study whether the coordinate dependence of the improved Self-Organizing Migrating Algorithm (iSOMA) can be reduced while retaining its inexpensive leader-directed migration mechanism. We introduce iSOMA-AR, which learns a basis from successful migration displacements and selectively applies the standard perturbation mask in that basis. On the complete noiseless BBOB suite, iSOMA- AR significantly outperformed baseline iSOMA across matched conditions, with the largest gains on geometrically difficult landscapes. A targeted ablation shows that the learned orientation is beneficial on a rotated ill-conditioned landscape and that moderate changes of the gate threshold and rotation cap preserve the qualitative result. On CEC 2011 Real World Optimization Problems, iSOMA-AR outperformed iL-SHADE on most problems, although its advantage over baseline iSOMA was not statistically significant. A canonical-jSO rerun is reported as a post-hoc sensitivity check alongside the original jSO-derived comparator. On frustrated-spin variational quantum objectives, adaptive rotation improved most transverse-field conditions, while gains on the diagonal and anisotropic models were absent or selective. Under strong effective sampling noise, the SOMA variants were the most robust population-based methods in the comparison, but iSOMA-AR was not significantly better than baseline iSOMA. Repairing all-zero PRT masks greatly reduced repeated-point evaluations without changing endpoint quality significantly, making this implementation detail unlikely to explain the noise result. Overall, adaptive rotation is most useful on coordinate-sensitive deterministic problems, while the observed noise robustness appears to arise mainly from the underlying SOMA migration mechanism.

Problem

• iSOMA
• coordinate dependence
• adaptive rotation
• variational quantum objectives
• optimization

Innovation

• Adaptive Rotation
• iSOMA-AR
• Basis Learning
• Noise Robustness
• Variational Quantum Objectives