Sequence Processing with Quantum Tensor Networks

We introduce complex-valued tensor network models for sequence processing motivated by correspondence to probabilistic graphical models, interpretability and resource compression. Inductive bias is introduced to our models via network architecture, and is motivated by the correlation structure inherent in the data, as well as any relevant compositional structure, resulting in tree-like connectivity. Our models are specifically constructed using parameterised quantum circuits, widely used in quantum machine learning, effectively using Hilbert space as a feature space. Furthermore, they are efficiently trainable due to their tree-like structure. We demonstrate experimental results for the task of binary classification of sequences from real-world datasets relevant to natural language and bioinformatics, characterised by long-range correlations and often equipped with syntactic information. Since our models have a valid operational interpretation as quantum processes, we also demonstrate their implementation on Quantinuum's H2-1 trapped-ion quantum processor, demonstrating the possibility of efficient sequence processing on near-term quantum devices. This work constitutes the first scalable implementation of near-term quantum language processing, providing the tools for large-scale experimentation on the role of tensor structure and syntactic priors. Finally, this work lays the groundwork for generative sequence modelling in a hybrid pipeline where the training may be conducted efficiently in simulation, while sampling from learned probability distributions may be done with polynomial speed-up on quantum devices.