Adiabatic Encoding of Pre-trained MPS Classifiers into Quantum Circuits
This work addresses training obstacles in quantum machine learning for classification tasks, offering a method to circumvent exponential hardness due to barren plateaus, though it is incremental in building on tensor-network embeddings.
The paper tackles the problem of training quantum neural networks (QNNs) by addressing barren plateaus and local minima through an adiabatic encoding framework that embeds pre-trained matrix product state (MPS) classifiers into quantum circuits, gradually removing postselection while maintaining performance, with numerical experiments on binary MNIST confirming robustness.
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 \emph{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.