Adaptive rotation improves quantum and classical optimization algorithm performance
Adaptive Rotation for iSOMA: Geometry, Benchmarking, and Noise Robustness in Variational Quantum Objectives
Neural and Evolutionary Computing
Summary
This paper looks at improving a certain type of optimization algorithm called iSOMA, which helps find good solutions to problems by moving around points in space. The authors present a version called iSOMA-AR that learns better directions to explore, especially helping on tricky landscapes that are rotated or stretched. They tested it on standard noisy and noiseless problems and on some quantum computing tasks, finding improvements mostly when problems are sensitive to the coordinate system. The new method remains robust against noise due to the underlying migration method it uses.
What this means in practice
- •For quantum algorithm engineers: Improve quantum variational algorithms by using adaptive rotation to enhance optimization on transverse-field problems.
- •For machine learning engineers: Use iSOMA-AR to optimize coordinate-sensitive deterministic problems more effectively compared to baseline methods.
Authors
Vojtěch Novák, Ivan Zelinka
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.