Spectral Anatomy of Quantum Gaussian Process Kernels

• URL: http://arxiv.org/abs/2605.30952v2
• Date: Tue, 02 Jun 2026 09:28:16 GMT
• Title: Spectral Anatomy of Quantum Gaussian Process Kernels
• Abstract summary: We prove a Cauchy-Schwarz tail bound on Nystrm approximation error, a finite-sample variance-contraction identity, and a characterization of the emphtarget-dependent optimal entropy.<n>The diagnostic is kernel-agnostic: hardware-efficient, matchgate, IQP emphand RBF/Matérn/RFF/deep- kernel families all collapse onto identical $S/log n$ curves.
• Score: 38.264196157340216
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Two recent results have reshaped quantum Gaussian processes (QGPs). On the one hand, \citet{lowe2025assessing} rule out the exponential speedups claimed by HHL-based QGP regression in the typical, well-conditioned regime; on the other, an independent line of work shows that highly expressive quantum kernels suffer posterior pathologies that break Bayesian optimization. We show that these seemingly unrelated phenomena are governed by the same quantity: the normalized spectral entropy $S(K)/\log n$ of the kernel Gram matrix. We prove a Cauchy--Schwarz tail bound on Nyström approximation error, a finite-sample variance-contraction identity in terms of Bach's degrees of freedom $d_σ(K)$, and a characterization of the \emph{target-dependent} optimal entropy via the intrinsic dimension of the target in the kernel eigenbasis. Empirically, the diagnostic is kernel-agnostic: hardware-efficient, matchgate, IQP \emph{and} RBF/Matérn/RFF/deep-kernel families all collapse onto identical $S/\log n$ curves on dequantization, ECE, and variance-contraction panels. The NLL sweet spot lives at high entropy for smooth targets and at low entropy for band-limited quantum-data targets. The diagnostic transfers from simulator to IBM Heron hardware with median absolute error $3.2\%$ and mean $5.2\%$ in $S/\log n$ across $24$ configurations at $n_q = 4$, with matchgate and IQP within $5\%$ mean and a single HE configuration returning a $30\%$ outlier that drops to $0.5\%$ on rerun (attributed to calibration drift); the same diagnostic transfers to a second Heron backend (mean error $2.7\%$) and to a $n_q = 6$ scale-up on the original backend (mean error $1.7\%$). No error mitigation is applied throughout.

Related papers

• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• Quantum PDE Solvers in Practice: Application-Driven Benchmarking of the Heat Equation [0.16999370482438728]
  We present a reproducible, application-driven benchmark for the 1-D Dirichlet heat equation.<n>The benchmark covers coherent linear solvers (HHL,VT, and QLS-Fourier), VQLS, imaginary-time methods (QITE, var-QITE, and AVQDS), real-time Hamiltonian simulation and unitary dilations.
  arXiv  Detail & Related papers  (2026-07-14T12:15:27Z)
• Active Quantum Kernel Acquisition for Gaussian Process Regression [30.032230630492155]
  Recent work on quantum kernel classification has shown that allocating shots non-uniformly across kernel entries can reduce the shot budget required to reach a target accuracy.<n>We extend this idea to Gaussian process (GP) regression, a setting whose downstream quantities (full-spectrum posterior variance, log-determinant, marginal likelihood) couple to kernel error more tightly than the sign-only outputs of classification.<n>We derive three closed-form pair-level sensitivities predictive coupling $|_i_j|$, leave-one-out residual, and marginal-likelihood gradient and plug them into a Neyman-style minimum
  arXiv  Detail & Related papers  (2026-06-27T09:40:20Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• Q-SINDy: Quantum-Kernel Sparse Identification of Nonlinear Dynamics with Provable Coefficient Debiasing [1.4323566945483497]
  Quantum feature maps offer expressive embeddings for classical learning tasks.<n>We introduce textbfQ-SINDy, a quantum kernelaugmented SINDy framework.<n>We identify a specific failure mode that arises: emphcoefficient cannibalization, in which quantum features absorb mass coefficient that rightfully belongs to the basis, corrupting equation recovery.
  arXiv  Detail & Related papers  (2026-04-18T02:00:27Z)
• Collective Kernel EFT for Pre-activation ResNets [0.20625936401496234]
  In finite-width deep neural networks, the empirical kernel $G$ evolvesally across layers.<n>We develop a collective kernel effective field theory (EFT) for pre-activation ResNets based on a $G$-only closure hierarchy and diagnose its finite closure window.
  arXiv  Detail & Related papers  (2026-04-17T06:31:50Z)
• Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without \textit{A Priori} Knowledge [0.0]
  We introduce emphblind CQEC, which estimates the target from the noisy output alone before catalytic recovery.<n>Five estimation strategies are benchmarked across three noise models.
  arXiv  Detail & Related papers  (2026-04-13T08:27:08Z)
• Sublinear Time Quantum Sensitivity Sampling [57.356528942341534]
  We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems.<n>Our framework provides a streamlined approach for constructing coresets and offers significant runtime improvements in applications such as clustering, regression, and low-rank approximation.
  arXiv  Detail & Related papers  (2025-09-20T20:18:49Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Differentially Quantized Gradient Methods [53.3186247068836]
  We show that Differentially Quantized Gradient Descent (DQ-GD) attains a linear contraction factor of $maxsigma_mathrmGD, rhon 2-R$. No algorithm within a certain class can converge faster than $maxsigma_mathrmGD, 2-R$.
  arXiv  Detail & Related papers  (2020-02-06T20:40:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.