6 October 2022 Thu 5 pm

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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 classical problems, like the evolution of cellular automata, and to quantum problems like predicting the evolution of a quantum state under the effects of an unknown external (possibly non-Markovian) environment.

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