Statevector-Referenced Geometry Survival of a Four-Qubit ZZ Quantum Kernel on IBM Quantum Hardware: A Fixed-Subset Diagnostic Across Three Execution Configurations
2026-07-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors tested how well a specific quantum method called a 'four-qubit ZZ feature-map kernel' kept its data structure when run on real quantum hardware with air-quality data. They tried three setups: the normal way, adding dynamical decoupling, and gate twirling, finding that gate twirling preserved the data structure best. However, even the best setup didn’t improve how well the quantum data matched the labels they wanted to predict. They concluded that while the hardware caused some changes, these changes didn't translate into better learning, and emphasized the need to measure both how faithfully quantum hardware runs algorithms and how well the tasks perform.
quantum kernel methodsGram matrixZZ feature-mapfour-qubit systemcentered kernel alignment (CKA)gate twirlingdynamical decouplingquantum hardware fidelityibm_fez backendquantum machine learning
Authors
Rostyslav Sipakov
Abstract
Quantum-kernel methods encode a dataset's geometry in a Gram matrix, so learning claims on hardware kernels assume the intended geometry survives execution. We measure that survival for one frozen four-qubit ZZ feature-map kernel on $N=24$ real indoor air-quality windows, reconstructed on ibm_fez (1024 shots per circuit) under baseline, dynamical decoupling alone, and gate twirling alone, each a single non-interleaved job. Every configuration returned a complete, finite, positive-semidefinite Gram matrix and preserved the centered statevector geometry to a substantial but incomplete descriptive degree (full-matrix centered kernel alignment, CKA, 0.933-0.989). Gate twirling was most faithful on every reported geometry axis, with the only jackknife-resolved improvement over baseline (persisted Spearman, mean absolute error, and full-matrix CKA diagnostics); dynamical decoupling alone was not separated from baseline at the frozen-window scale. Residual hardware distortion, not finite sampling, dominates the discrepancy. Yet fidelity and label alignment were reversed: the most faithful configuration had the lowest centered kernel-target alignment, which sits at or below label-permutation references for statevector and hardware alike. We read the small hardware uplift as a normalization property of the non-affine distortion, not captured signal. These are descriptive results for single jobs on one backend, not causal mitigation-efficacy estimates; no quantum-advantage, hardware-classifier-superiority, or forecasting claim is made. Implementation fidelity and task relevance are distinct axes; hardware quantum machine-learning studies should report both.