The clearest gains from a modified optimization algorithm appeared on benchmark problems whose results depend strongly on the geometry of the search space. Across 720 matched BBOB conditions, iSOMA-AR beat baseline iSOMA 507 times, tied 42 times and lost 171 times. Its median condition-wise error ratio was about 0.81. In a separate target test, it reached targets in 36.4% of run-target pairs, compared with 29.5% for baseline. The improvement came with about 12% more optimizer time per 1,000 evaluations.
What the modified optimizer does
The change is designed to reduce iSOMA's dependence on the coordinate system used to describe a problem while preserving its leader selection, path construction, acceptance rule and evaluation budget. iSOMA-AR builds a success matrix from normalized movements that strictly improve the objective. A gated set of directions derived from that matrix is then used for occasional rotated PRT masking, changing the geometry of proposed moves without adding objective evaluations.
The primary BBOB protocol covered 24 noiseless functions at dimensions 5, 10 and 20, instances 1 through 5, and budgets of 500D and 2,000D, with 10 runs per condition and 36,000 recorded runs. CEC added 22 real-world problems, a 50,000-evaluation budget, 10 runs per problem and 1,100 recorded runs. The analysis compared paired wins, ties and losses and used paired Wilcoxon signed-rank tests on log-scaled error or regret ratios with Holm correction. Because conditions from the same benchmark functions were not fully independent, the BBOB and CEC p-values were treated as descriptive.
The clearest edge came on BBOB
The overall BBOB comparison favored the adaptive version across the full set of matched conditions. Its target-hit fraction also rose at the tightest reported target, from 12.2% for baseline iSOMA to 15.5% for iSOMA-AR. These gains came with a modest increase in optimizer-side runtime rather than a larger objective-evaluation budget.
The strongest reductions appeared in conditioning-sensitive groups. The AR-to-baseline median error ratio was 0.55 for low or moderate conditioning and 0.45 for high-conditioning unimodal functions, where iSOMA-AR won 137 of 150 conditions. A targeted ablation found that the learned basis outperformed both baseline iSOMA and a random-basis control on rotated Ellipsoid, while Rastrigin showed no corresponding advantage. Because the ablation covered a targeted set of landscapes, it does not establish the same benefit everywhere.
Other tests were less uniform
The CEC 2011 results were more restrained. On 22 real-world problems under a 50,000-evaluation budget, iSOMA-AR had a mean rank of 3.27 versus 3.41 for baseline iSOMA. It won 11 problems, tied three and lost eight; the Holm-adjusted p-value was 0.34. Against iL-SHADE, it won 14, tied two and lost six, with a median regret ratio of about 0.125 and p = 0.052. That makes the method competitive in this panel, not a statistically established improvement over baseline. Four CEC problems were flagged as provisional because of implementation or reference discrepancies.
The VQE tests also resisted a single verdict. Exact runs used budgets of 10,000 and 30,000 evaluations, with 25 independent seed labels and 25 runs per optimizer. On Q2, iSOMA-AR's median final error was 24% to 48% lower across four conditions, with significant direct comparisons in three. Q1 showed no benefit, while Q3 improved only at the larger budget.
Under high effective noise, set at M = 128 effective shots, iSOMA-AR had the best mean rank across six model-budget conditions, 1.83 versus 2.17 for iSOMA, and ranked first or second in every condition. Yet no direct AR-to-baseline comparison was statistically significant. The median selection penalty was 0.381 for iSOMA-AR versus 0.313 for baseline. Because the noise model was an effective Gaussian surrogate rather than a hardware measurement model, the result does not show that adaptive rotation itself explains the high-noise performance.
A narrower conclusion
One control addressed an implementation detail. Repairing all-zero PRT masks reduced unchanged-point evaluations, but none of eight paired Q1 and Q2 endpoint comparisons was significant; every Wilcoxon p-value was at least 0.252. In those conditions, the repair reduced repeated evaluations without materially changing endpoint quality.
Taken together, the evidence points to a specific use case: deterministic optimization with rotated or coupled geometry. The BBOB result was broad, but CEC was less decisive, and VQE performance changed with the model and budget. High-noise VQE also did not establish a unique benefit from adaptive rotation. The study does not show that iSOMA-AR is universally superior to baseline iSOMA or the other comparators.
Paper data and sources
Original title: Adaptive Rotation for iSOMA: Geometry, Benchmarking, and Noise Robustness in Variational Quantum Objectives
Authors: Vojtěch Novák, Ivan Zelinka
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-29
DOI: Not available
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