  Many complex chemical problems encoded in terms of physics-based models
become computationally intractable for traditional numerical approaches due to
their unfavourable scaling with increasing molecular size. Tensor decomposition
techniques can overcome such challenges by decomposing unattainably large
numerical representations of chemical problems into smaller, tractable ones. In
the first two decades of this century, algorithms based on such tensor
factorizations have become state-of-the-art methods in various branches of
computational chemistry, ranging from molecular quantum dynamics to electronic
structure theory and machine learning. Here, we consider the role that tensor
decomposition schemes have played in expanding the scope of computational
chemistry. We relate some of the most prominent methods to their common
underlying tensor network formalism, providing a unified perspective on leading
tensor-based approaches in chemistry and materials science.
