A PAC-Bayesian approach to generalization for quantum models

• URL: http://arxiv.org/abs/2603.22964v1
• Date: Tue, 24 Mar 2026 08:58:54 GMT
• Title: A PAC-Bayesian approach to generalization for quantum models
• Abstract summary: We provide the first PAC-Bayesian generalization bounds for a broad class of quantum models.<n>This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning.
• Score: 0.9543943371833464
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning.

Related papers

• Asymptotic Expansions for Neural Network Approximations of Quantum Channels [0.0]
  This paper establishes the Quantum Voronovskaya--Damasclin (QVD) Theorem, providing a complete characterization of Quantum Neural Network Operators.<n>We introduce quantum analogues of Sobolev and Hlder spaces defined through Fréchet differentiability in the Liouville representation.<n>Within this framework, we derive an explicit expansion of the approximation error and identify the fundamental mechanisms governing convergence.
  arXiv  Detail & Related papers  (2026-03-09T18:12:57Z)
• Quantum LEGO Learning: A Modular Design Principle for Hybrid Artificial Intelligence [63.39968536637762]
  We introduce Quantum LEGO Learning, a learning framework that treats classical and quantum components as reusable, composable learning blocks.<n>Within this framework, a pre-trained classical neural network serves as a frozen feature block, while a VQC acts as a trainable adaptive module.<n>We develop a block-wise generalization theory that decomposes learning error into approximation and estimation components.
  arXiv  Detail & Related papers  (2026-01-29T14:29:21Z)
• Towards A Unified PAC-Bayesian Framework for Norm-based Generalization Bounds [63.47271262149291]
  We propose a unified framework for PAC-Bayesian norm-based generalization.<n>The key to our approach is a sensitivity matrix that quantifies the network outputs with respect to structured weight perturbations.<n>We derive a family of generalization bounds that recover several existing PAC-Bayesian results as special cases.
  arXiv  Detail & Related papers  (2026-01-13T00:42:22Z)
• Path integral approach to quantum thermalization [39.25860941747971]
  We introduce a quasiclassical Green function approach describing the unitary yet irreversible dynamics of quantum systems.<n>We show that it is capable of describing a wide range of system classes and disorder models.<n>We present our formalism in a self-contained and pedagogical manner, aiming to provide a transferable toolbox for the first-principles description of many-body chaotic quantum systems.
  arXiv  Detail & Related papers  (2025-09-07T12:10:48Z)
• Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise [0.0]
  This study investigates the generalization properties of parameterized quantum machine learning models under the influence of noise.<n>We present a data-dependent generalization bound grounded in the quantum Fisher information matrix.<n>We provide a structured characterization of complexity in quantum models by integrating local parameter neighborhoods and effective dimensions defined through quantum Fisher information matrix eigenvalues.
  arXiv  Detail & Related papers  (2024-12-16T05:10:58Z)
• Understanding quantum machine learning also requires rethinking generalization [0.3683202928838613]
  We show that traditional approaches to understanding generalization fail to explain the behavior of quantum models. Experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data.
  arXiv  Detail & Related papers  (2023-06-23T12:04:13Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Bandwidth Enables Generalization in Quantum Kernel Models [16.940180366663903]
  Recent results show that generalization of quantum models is hindered by the exponential size of the quantum feature space. We show that changing the value of the bandwidth can take a model from provably not being able to generalize to any target function to good generalization for well-aligned targets.
  arXiv  Detail & Related papers  (2022-06-14T08:41:08Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

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.