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

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 disentangling variational method leveraging standard tensor network optimization techniques and (2) an 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.