Abstract
The method of choice to study one-dimensional strongly interacting many-body quantum systems is based on matrix product states and operators. Such a method allows one to explore the most relevant and numerically manageable portion of an exponentially large space. It also allows one to accurately describe 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 a bidirectional, long, short-term-memory neural network. To highlight the flexibility of the algorithm, we also show that it can readily perform classification tasks.