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Classical neural networks on quantum devices via tensor network disentanglers: A case study in image classification

Borja Aizpurua1,2,*, Sukhbinder Singh3, and Román Orús1,4,5

  • *Contact author: borja.aizpurua@multiversecomputing.com
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Phys. Rev. Research 8, 023030 – Published 8 April, 2026

DOI: https://doi.org/10.1103/fmps-tjwy

Abstract

We address the problem of implementing bottleneck layers from classical pretrained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid classical-quantum models. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the disentangling circuits are deployed on a quantum computer while the remainder of the network—including the disentangled MPO—runs on classical hardware. We introduce two complementary algorithms for MPO disentangling: (1) an explicitly disentangling variational method leveraging standard tensor network optimization techniques and (2) an implicitly disentangling gradient-descent-based approach. We validate these methods through a proof-of-concept translation of simple classical neural networks for MNIST and CIFAR-10 image classification into a hybrid classical-quantum form.

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Phys. Rev. Research 8, 023030– Published 8 April, 2026
  • Received 18 September 2025
  • Accepted 12 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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