Statevector-Referenced Geometry Survival of a Four-Qubit ZZ Quantum Kernel on IBM Quantum Hardware: A Fixed-Subset Diagnostic Across Three Execution Configurations

תקציר מקורי באנגליתarXiv:2607.20377v1 Announce Type: cross 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 jac