Fractal dimension predicts quantum kernel collapse in angle-encoded data
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
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arXiv: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.
The study reports on three separate executions of a four‑qubit ZZ feature map on the ibm_fez backend, each using 1024 shots per circuit. The authors compare the resulting hardware‑reconstructed Gram matrices to an exact statevector reference, finding off‑diagonal RMSE values of 0.0878, 0.0864, and 0.0427 for the baseline, dynamical decoupling, and gate‑twirling jobs respectively, and centered kernel alignment scores ranging from 0.933 to 0.989. The gate‑twirling job shows the smallest deviation across all metrics, while the baseline job’s contrasts remain stable under deletion‑stable diagnostics; the study notes that sampling alone cannot explain the observed errors and that implementation fidelity and task relevance are distinct diagnostic axes.
arXiv:2607. 19782v1 Announce Type: cross Abstract: Kernel methods are powerful tools in machine learning but commonly used full-Gram kernels face three key limitations: (1) quadratic scaling with training set size; (2) the use of fixed, non-trainable kernels; and (3) the absence of an intrinsic formulation for multiclass classification.
arXiv:2510. 03389v2 Announce Type: replace-cross Abstract: Current quantum computers require algorithms that use limited resources economically.
arXiv:2605. 30952v2 Announce Type: replace Abstract: Two recent results have reshaped quantum Gaussian processes (QGPs).
arXiv:2607. 11936v1 Announce Type: new Abstract: Hyperdimensional Computing (HDC) represents symbols using high-dimensional hypervectors of dimension $D$.