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 pre-trained 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: (i) an explicitly disentangling variational method leveraging standard tensor-network optimization techniques, and (ii) 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.