Leakage-Controlled Projected Quantum Kernels for Orbital Conjunction Risk Assessment Using SOCRATES Data
- 1Department of Computer Science and Engineering, University of Bologna, 40126 Bologna, Italy
- 2Rosen Center for Advanced Computing, Purdue University, West Lafayette, IN 47907, USA
- 3Department of Computer Engineering, Gachon University, Seongnam-si 13120, Republic of Korea
Abstract
Conjunction assessment needs risk screening that is early, scalable and interpretable. We ask whether projected quantum feature maps add predictive value to this task when compared with strong classical learners under strict leakage control. From 149,044 real SOCRATES conjunction events (119,568 object pairs), split pair-disjointly, we predict the base-ten logarithm of the maximum collision probability. We prove that the pair-disjoint held-out loss is unbiased for the risk on unseen pairs, that the logarithmic target preserves risk ranking, that the local six-qubit feature map is exactly a classical additive model, and when a validation-fitted ensemble assigns a member zero weight. In the configuration fixed a priori (encoding bandwidth π, linear outer kernel), the projected models trail gradient boosting (RMSE 0.668 and 0.762 against 0.602), and the local map is no better than a linear ridge on the raw inputs. Matched experiments on identical training sets show that this shortfall comes from two design choices rather than from the representation: the bandwidth folds the dominant descriptors, and the linear outer kernel discards nonlinear structure. With a validated bandwidth and a Gaussian outer kernel, the local projected model outperforms a tuned classical Gaussian kernel on 1200-event subsets in all five draws (0.641±0.003) and has the lowest point estimate at full scale (0.589), where it is statistically tied with that kernel. It takes the largest weight in an ensemble that lowers RMSE from 0.599 to 0.579. This is not a quantum advantage: the local model is classically computable in closed form, and the interaction pattern of the entangled variant never improves accuracy. In 200 randomly seeded configurations at B=π and B=π/4, it reduces it, and at the validated bandwidth the difference is not significant at full scale.
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BibTeX
@article{arshad2026leakagecontrolled,
title = {{Leakage-Controlled Projected Quantum Kernels for Orbital Conjunction Risk Assessment Using SOCRATES Data}},
author = {Muhammad Waqas Arshad and David Q. Liu and Syed Rizwan Hassan},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203774},
url = {https://www.mdpi.com/2227-7390/14/20/3774},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Leakage-Controlled Projected Quantum Kernels for Orbital Conjunction Risk Assessment Using SOCRATES Data
AU - Muhammad Waqas Arshad
AU - David Q. Liu
AU - Syed Rizwan Hassan
PY - 2026
DA - 2026/10/17
JO - Mathematics
DO - 10.3390/math14203774
UR - https://www.mdpi.com/2227-7390/14/20/3774
AB - Conjunction assessment needs risk screening that is early, scalable and interpretable. We ask whether projected quantum feature maps add predictive value to this task when compared with strong classical learners under strict leakage control. From 149,044 real SOCRATES conjunction events (119,568 object pairs), split pair-disjointly, we predict the base-ten logarithm of the maximum collision probability. We prove that the pair-disjoint held-out loss is unbiased for the risk on unseen pairs, that the logarithmic target preserves risk ranking, that the local six-qubit feature map is exactly a classical additive model, and when a validation-fitted ensemble assigns a member zero weight. In the configuration fixed a priori (encoding bandwidth π, linear outer kernel), the projected models trail gradient boosting (RMSE 0.668 and 0.762 against 0.602), and the local map is no better than a linear ridge on the raw inputs. Matched experiments on identical training sets show that this shortfall comes from two design choices rather than from the representation: the bandwidth folds the dominant descriptors, and the linear outer kernel discards nonlinear structure. With a validated bandwidth and a Gaussian outer kernel, the local projected model outperforms a tuned classical Gaussian kernel on 1200-event subsets in all five draws (0.641±0.003) and has the lowest point estimate at full scale (0.589), where it is statistically tied with that kernel. It takes the largest weight in an ensemble that lowers RMSE from 0.599 to 0.579. This is not a quantum advantage: the local model is classically computable in closed form, and the interaction pattern of the entangled variant never improves accuracy. In 200 randomly seeded configurations at B=π and B=π/4, it reduces it, and at the validated bandwidth the difference is not significant at full scale.
SN - 2227-7390
ER -