Researchers have evaluated the fidelity of a four-qubit ZZ quantum kernel's geometry on IBM quantum hardware, specifically the ibm_fez processor. The goal was to determine how execution on real hardware preserves the data geometry encoded in a Gram matrix, a crucial aspect for the reliability of quantum machine learning methods. Twenty-four windows of indoor air quality data were used, with each circuit executed with 1024 shots under three configurations: a baseline, dynamical decoupling, and gate twirling.

All configurations yielded complete, finite, positive-semidefinite Gram matrices, preserving the centered statevector geometry to a substantial, though incomplete, degree. The full-matrix centered kernel alignment (CKA) metric ranged from 0.933 to 0.989. Gate twirling proved to be the most faithful technique across all reported geometric axes, being the only one to show a statistically significant improvement over the baseline. In contrast, dynamical decoupling did not separate from the baseline at the frozen-window scale. The results suggest that residual hardware distortion, rather than finite sampling, dominates the discrepancy.

Interestingly, the most faithful configuration in terms of geometric preservation showed the lowest centered kernel-target alignment, indicating that implementation fidelity and task relevance are distinct axes. This finding underscores the importance of reporting both factors in hardware quantum machine learning studies. The authors emphasize that these are descriptive results for single jobs on a specific backend and do not imply quantum advantage, hardware classifier superiority, or forecasting capabilities.