A preprint comparing quantum feature maps across five binary-classification datasets found no single winner. The encoding that produced the strongest raw test scores on one dataset could carry a heavier circuit and simulation burden, or lose more ground between training and test data. When those trade-offs were counted together, the preferred method changed by dataset.
The study asked whether incorporating statistical relationships among classical features would change quantum support vector machine, or QSVM, performance. In the dependency-aware design, individual features were encoded with RY rotations, while pairwise relationships were represented with CRY gates. The analysis tested Pearson and Spearman correlation, Kendall's Tau, Mutual Information and Distance Correlation alongside standard encodings.
The benchmark covered five Kaggle binary-classification datasets: EEG eye state, heart failure, credit risk, student performance and Alzheimer's disease. Reported configurations included a balanced EEG subset of 2,000 samples with 14 features; 918 original Heart Failure observations with 10 retained features; 1,000 Credit Risk observations with nine features; and 13 Student Performance input variables after GPA-derived labeling and removal of GPA. The Alzheimer description listed 2,149 patient records, then retained the first 14 principal components for quantum encoding.
The winner depended on the dataset
On EEG, the full ZZ configuration led the raw results: test accuracy was 0.850, F1-score was 0.817 and ROC-AUC was 0.928. But it also had an approximately 0.150 training-test accuracy gap, 301 logical gates, circuit depth 77 and 126.6 seconds of state-vector time. ZZ circular reached 0.846 accuracy with 70 gates and about 28 seconds, making it nearly as accurate at a much lower reported cost.
On Heart Failure, the Pearson- and Distance Correlation-based RY+CRY variants shared the highest test accuracy, 0.883. Z Feature Map was close at 0.878 and had a 0.016 accuracy gap. ZZ circular, however, posted 0.994 training accuracy against 0.757 on test data, a gap of 0.238. The figures show why the study tracked the training-test gap as well as test accuracy.
Credit Risk produced a different pattern. Every encoding had the same label-based test Accuracy, 0.908, Precision, 0.824, Recall, 0.908, and F1, 0.864. Yet the reported ROC-AUC still separated the methods: Distance Correlation-based RY+CRY reached 0.663, while Z Feature Map was lowest at 0.464. Here, the encoding choice changed the ROC-AUC ranking even though the other listed test metrics were identical.
Student Performance favored the Z Feature Map. It recorded test accuracy of 0.944, F1 of 0.900 and ROC-AUC of 0.975, with a 0.024 accuracy gap, 26 logical gates and circuit depth 2. ZZ full reached 1.000 training accuracy but only 0.712 on test data; its test Recall was 0.020, F1 was 0.040 and gap was 0.288. The full ZZ model therefore paired a perfect training score with much weaker reported test results.
After PCA, the Alzheimer analysis retained 14 components explaining approximately 49.61% of the variance. Angle-RY, H+RY and Pearson RY+CRY tied for the best test accuracy, 0.764, F1, 0.612, and ROC-AUC, 0.813. ZZ linear and ZZ circular had test F1 scores of zero. ZZ full had approximately 0.65 test accuracy, but Recall was 0.011 and F1 was 0.022. The result reflects this particular combination of PCA and encoding choices, rather than an encoding-only comparison.
Raw scores were only part of the story
To combine these dimensions, the study used the Quantum Feature Encoding Score, or QFES. The composite combines five test classification measures with the training-test accuracy gap and within-dataset normalized circuit depth, gate count and state-vector time. The generalization and cost terms are scaled per input, so a method is not rewarded simply for a high test score if it also carries a large gap or expensive computation.
That broader score changed the ranking. Z Feature Map ranked first for EEG and Student Performance, while Angle-RY ranked first for Heart Failure, Credit Risk and Alzheimer's disease. The pattern reinforces the study's central result: raw performance and overall efficiency did not always point to the same encoding.
A controlled simulation with clear limits
The comparison used ideal state-vector simulations on a classical computer, not a physical quantum processing unit. For each method, the study computed squared-overlap quantum kernels and supplied them to a support vector machine, using the same preprocessing and train-test split within each dataset. The benchmark therefore describes behavior in a controlled simulation setting, not performance on physical hardware.
The benchmark reports point estimates, but no confidence intervals or repeated-split variability estimates. The document identifies itself as arXiv:2608.27764v1, dated 27 Aug 2026. The findings are therefore an initial computational comparison whose rankings should be read in the context of the reported datasets, preprocessing and splits.
Paper data and sources
Original title: Benchmarking Quantum Feature Encoding Strategies for Binary Classification with QSVM
Authors: Murat Kurt
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-27
DOI: Not available
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