Learnable yet not simulable: a quantum resource theory of learning models

• URL: http://arxiv.org/abs/2608.02325v1
• Date: Mon, 03 Aug 2026 14:48:03 GMT
• Title: Learnable yet not simulable: a quantum resource theory of learning models
• Abstract summary: It remains unclear which quantum resource governs the classical learnability of quantum circuits.<n>We study the expectation-value functions of families of tunable quantum circuits.<n>These results establish a quantitative resource-theoretic framework for delineating the boundary between classical simulation and learning.
• Score: 57.695822250391906
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum resource theory has sharpened our understanding of the intrinsic complexity of quantum systems, particularly their classical simulability. However, it remains unclear which quantum resource governs the classical learnability of quantum circuits, especially beyond the regime of efficient classical simulation. Here we close this knowledge gap by studying the expectation-value functions of families of tunable quantum circuits, with many applications in digital quantum simulation, quantum metrology, and quantum-system characterization. Specifically, we introduce a new resource measure, the dynamical stabilizer entropy (\DSE), which quantifies how broadly an expectation-value function is distributed across its frequency modes. By relating \DSE to operator stabilizer entropy, we establish a computational phase diagram that compares classical simulators with quantum-data-assisted classical surrogates. We first determine the \DSE-dependent learnability boundary of this diagram by deriving bounds on the sample complexity and runtime of classical surrogates, and by developing a \DSE-guided surrogate. We then complete the diagram by proving, under standard complexity-theoretic assumptions, the existence of circuit families that can be efficiently learned by this surrogate but cannot be efficiently emulated from their circuit descriptions alone. Numerical experiments on random and structured circuits with up to 80 qubits support the predicted \DSE-dependent computational landscape. These results establish a quantitative resource-theoretic framework for delineating the boundary between classical simulation and learning, motivate resource measures linking quantum resources to learnability, and guide the design of learning-based algorithms for scalable quantum systems beyond the reach of direct classical simulation.

Related papers

• The cost of simulating classically tractable quantum circuits and dynamics [0.0]
  simulability is a statement, and does not by itself determine whether the (quantum-inspired) classical simulation is actually practical. Indeed, different scalings can ask whether classically simulable quantum dynamics are in practice more resource-efficient to simulate classically than to execute directly on quantum hardware.<n>Our work indicates that guarantees of classical simulability with resources alone are insufficient to determine the preferred implementation.
  arXiv  Detail & Related papers  (2026-09-10T17:34:39Z)
• Comparing Classical Simulation and Sample-Based Learning of Quantum Systems: Learning the Hardness of Quantum Systems from Samples [41.99844472131922]
  We investigate the relationship between two distinct classical approaches to quantum systems.<n>We use a fixed deep energy-based generative model trained on measurement samples from controlled families of quantum states.
  arXiv  Detail & Related papers  (2026-05-27T18:44:36Z)
• Hybrid Classical-Quantum Transfer Learning with Noisy Quantum Circuits [0.0]
  We introduce a family of compact quantum transfer learning architectures for image classification.<n>We instantiate and evaluate several classical-quantum hybrid models implemented in PennyLane and Qiskit.<n> Experimental results show that the proposed quantum transfer learning architectures achieve competitive and, in several cases, superior accuracy.
  arXiv  Detail & Related papers  (2026-03-17T12:28:33Z)
• 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)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [50.95799256262098]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience.<n>We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Provably Efficient Adiabatic Learning for Quantum-Classical Dynamics [4.381980584443765]
  We develop a generic theoretical framework for analyzing quantum-classical adiabatic dynamics with learning algorithms. Based on quantum information theory, we develop a provably efficient adiabatic learning (PEAL) algorithm with logarithmic system size sampling complexity. We benchmark PEAL on the Holstein model, and demonstrate its accuracy in predicting single-path dynamics and ensemble dynamics observables as well as transfer learning over a family of Hamiltonians.
  arXiv  Detail & Related papers  (2024-08-01T04:31:36Z)
• Lie-algebraic classical simulations for quantum computing [0.3774866290142281]
  We present a framework for classical simulations, dubbed "$mathfrakg$-sim"<n>We show that $mathfrakg$-sim enables new regimes for classical simulations.<n>We report large-scale noiseless and noisy simulations on benchmark problems.
  arXiv  Detail & Related papers  (2023-08-02T21:08:18Z)
• Tensor Networks or Decision Diagrams? Guidelines for Classical Quantum Circuit Simulation [65.93830818469833]
  tensor networks and decision diagrams have independently been developed with differing perspectives, terminologies, and backgrounds in mind. We consider how these techniques approach classical quantum circuit simulation, and examine their (dis)similarities with regard to their most applicable abstraction level. We provide guidelines for when to better use tensor networks and when to better use decision diagrams in classical quantum circuit simulation.
  arXiv  Detail & Related papers  (2023-02-13T19:00:00Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)

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.