Revisiting the Classics: Turning Old Ideas into New Methods with Tensor Networks

A key challenge for computation is solving problems in high dimensions. Two classic proposals for tackling high dimensional problems are the Bethe approximation, or "belief propagation", and the quantum Fourier transform. Tensor networks offer a newer perspective on high-dimensional problems. Yet these diverse ideas are arguably tailor made for each other and when combined are starting to crack problems that seemed forbidding just a few years ago. Applications include solving high-dimensional differential equations and continuum functions as well as simulations of quantum circuits and dynamics on 2D and 3D lattices.