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Multivariate functions of continuous variables arise in countless branches ofscience. Numerical computations with such functions typically involve acompromise between two contrary desiderata: accurate resolution of thefunctional dependence, versus parsimonious memory usage. Recently, twopromising strategies have emerged for satisfying both requirements: (i) Thequantics representation, which expresses functions as multi-index tensors, witheach index representing one bit of a binary encoding of one of the variables;and (ii) tensor cross interpolation (TCI), which, if applicable, yieldsparsimonious interpolations for multi-index tensors. Here, we present astrategy, quantics TCI (QTCI), which combines the advantages of both schemes.We illustrate its potential with an application from condensed matter physics:the computation of Brillouin zone integrals.

Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond