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Quantum Convolutional Neural Networks are Effectively Classically Simulable

Pablo Bermejo1,2,3, Paolo Braccia4, Manuel S. Rudolph5, Zoë Holmes5, Lukasz Cincio4, and M. Cerezo1,*

  • *Contact author: cerezo@lanl.gov
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PRX Quantum 7, 020304 – Published 6 April, 2026

DOI: https://doi.org/10.1103/8qt9-72ts

Abstract

Quantum convolutional neural networks (QCNNs) are widely regarded as a promising model for quantum machine learning (QML). In this work, we analyze the most widely used variants of these models (i.e., tracing out- and measurement-based QCNNs), and we relate their heuristic success to two facts. First, that when randomly initialized, they can only operate on the information encoded in low-bodyness measurements of their input states. And second, that they are commonly benchmarked on “locally easy” datasets whose states are precisely classifiable by the information encoded in these low-bodyness observables subspace. From these insights, we argue that the QCNN’s action on this subspace should be efficiently classically simulable. Indeed, we construct and train a purely classical QCNN surrogate—based on low-bodyness Pauli propagation, tensor networks, and classical shadows—that matches or outperforms standard QCNNs on all benchmark datasets and on up-to 1024 qubits, thereby empirically realizing our simulability claims. Our results can then be understood as highlighting a deeper symptom of QML: Models could only be showing heuristic success because they are benchmarked on simple problems, for which their action can be classically simulated. This insight points to the fact that nontrivial datasets are a truly necessary ingredient for moving forward with QML. To finish, we discuss how our results can be extrapolated to classically simulate other architectures.

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Popular Summary

Quantum convolutional neural networks (QCNNs) are widely regarded as one of the most promising architectures in quantum machine learning. Inspired by classical convolutional neural networks, QCNNs have been used to classify both classical data and complex quantum states, including phases of matter. Their apparent trainability and strong benchmark performance have positioned them as leading candidates for near-term quantum advantage.

In this work, we take a closer look at why QCNNs succeed—and arrive at a surprising conclusion. We show that commonly studied QCNN architectures effectively operate only on low-bodyness (i.e., local) observables of their input states, especially when randomly initialized. At the same time, the datasets used to demonstrate their power-ranging from condensed matter systems to standard image classification benchmarks—turn out to be “locally easy”: their relevant features are already encoded in these same local observables.

These two observations together imply that QCNNs can be efficiently simulated on classical computers. We make this concrete by constructing purely classical surrogate models based on low-bodyness Pauli propagation, tensor networks, and classical shadow tomography. These classical surrogates match or even outperform full QCNNs across all tested benchmarks, including systems with up to 1024 qubits—while requiring dramatically fewer quantum resources.

Our results suggest that the heuristic success of QCNNs stems not from uniquely quantum information processing, but from the simplicity of the benchmark problems themselves. Moving forward, demonstrating genuine quantum advantage will require identifying nontrivial datasets that cannot be captured within classically simulable regimes.

Article Text

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PRX Quantum 7, 020304– Published 6 April, 2026
  • Received 22 October 2024
  • Accepted 19 February 2026
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