  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.

Quantum Physics