aiqbench analysis
This study provides a rigorous diagnostic of how hardware noise distorts the geometric structure of quantum kernels on IBM's ibm_fez backend, distinguishing between residual distortion and finite sampling effects. While gate twirling best preserved statevector geometry in this specific frozen-window setup, it did not necessarily improve alignment with classification labels, highlighting that implementation fidelity does not always correlate directly with task performance. The findings underscore the necessity for quantum ML researchers to independently report both hardware-level geometric preservation and actual label alignment when evaluating mitigation strategies on real devices.
Statevector-Referenced Geometry Survival of a Four-Qubit ZZ Quantum Kernel on IBM Quantum Hardware: A Fixed-Subset Diagnostic Across Three Execution Configurations
arXiv:2607.20377v1 Announce Type: new 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.
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.
3 supplementary notes. Code and data available at Zenodo: this https URL. Preprint also available at this http URL: this https URL
Quantum Physics (quant-ph); Machine Learning (cs.LG)
I.2.6; I.5.2; F.2.1
arXiv:2607.20377 [quant-ph]
(or arXiv:2607.20377v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.20377 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 340 words
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