Adiabatic Encoding of Pre-trained MPS Classifiers into Quantum Circuits

Although Quantum Neural Networks (QNNs) offer powerful methods for classification tasks, the training of QNNs faces two major training obstacles: barren plateaus and local minima. A promising solution is to first train a tensor-network (TN) model classically and then embed it into a QNN. However, embedding TN-classifiers into quantum circuits generally requires postselection whose success probability may decay exponentially with the system size. We propose an adiabatic encoding framework that encodes pre-trained MPS-classifiers into quantum MPS (qMPS) circuits with postselection, and gradually removes the postselection while retaining performance. We prove that training qMPS-classifiers from scratch on a certain artificial dataset is exponentially hard due to barren plateaus, but our adiabatic encoding circumvents this issue. Additional numerical experiments on binary MNIST also confirm its robustness.