Four-Qubit Kernel Preserves Geometry on IBM Quantum Hardware to 98.9%
Rostyslav Sipakov of Kyiv National University of Construction and Architecture has demonstrated a centered kernel alignment (CKA) ranging from 0.933 to 0.989 within a four-qubit quantum kernel executed on IBM’s ibm_fez hardware, despite known imperfections in the system. The research measured this using full-matrix centered kernel alignment, revealing a substantial but incomplete degree of geometry preservation given the inherent challenges of near-term quantum devices. While dynamical decoupling alone was not distinguishable from baseline at the frozen-window scale, gate twirling demonstrably enhanced geometry preservation across multiple diagnostic metrics. The most faithful configuration had the lowest centered kernel, target alignment, a reversal of expectations suggesting a complex interplay between hardware distortion and signal recovery; as the paper states, these are “descriptive results for single jobs on one backend, not causal mitigation-efficacy estimates.” A substantial degree of geometric preservation was observed, with full-matrix centered kernel alignment (CKA) scores ranging from 0.933, 0.989. This work focused on reconstructing the kernel geometry, rather than assessing any potential quantum advantage in a downstream task, establishing a baseline for future studies. The research team employed three execution configurations: a baseline, dynamical decoupling alone, and gate twirling alone, to assess noise mitigation strategies. Dynamical decoupling alone was not separated from baseline at the frozen-window scale, while gate twirling improved geometry preservation, showing jackknife-resolved improvements in Spearman correlation, mean absolute error, and full-matrix CKA diagnostics. The most faithful configuration had the lowest centered kernel, target alignment, even falling below reference points for both statevector and hardware. The team interprets this reversal as a normalization property of hardware distortion, suggesting a complex relationship b
