  The method of choice to study one-dimensional strongly interacting many body
quantum systems is based on matrix product states and operators. Such method
allows to explore the most relevant, and numerically manageable, portion of an
exponentially large space. It also allows to describe accurately correlations
between distant parts of a system, an important ingredient to account for the
context in machine learning tasks. Here we introduce a machine learning model
in which matrix product operators are trained to implement sequence to sequence
prediction, i.e. given a sequence at a time step, it allows one to predict the
next sequence. We then apply our algorithm to cellular automata (for which we
show exact analytical solutions in terms of matrix product operators), and to
nonlinear coupled maps. We show advantages of the proposed algorithm when
compared to conditional random fields and bidirectional long short-term memory
neural network. To highlight the flexibility of the algorithm, we also show
that it can readily perform classification tasks.
