Jan von Delft | Quantics Tensor Cross Interpolation

▶Title: Quantics Tensor Cross Interpolation: a Quantum-Inspired Tools for Manipulating Functions
▶Speaker: Jan von Delft (LMU)
▶Abstract: Tensor network techniques are well-established numerical tools for solving seemingly exponentially hard problems in quantum many-body physics. They rely on a form of data compression for many-body wavefunctions in which tensors with many indices are expressed through networks involving tensors of low rank; prominent examples are tensor trains (TTs) (also known as matrix product states). Low-rank TTs provide exponential reductions in computational complexity. Currently, two paradigm shifts are unfolding that expand the range of tensor network applications into many other branches of computational science. First, new exponentially fast machine learning algorithms are emerging for finding accurate TT representations of huge but compressible tensors. These algorithms learn compact representations of the entire object from a tiny training data set. Second, it is becoming apparent that tensors arising from discretizing mathematical functions, such as the solutions of partial differential equations, are often compressible too, admitting low-rank TT representations. These “quantum-inspired” representations enable manipulations of functions (integration, convolution, Fourier transform, ...) to be performed exponentially faster. Together, these two developments offer numerous opportunities for exponential cost reductions in computational science.

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