Robust numerical algorithms for electronic structure calculation using the quantized TT decomposition

The idea of reshaping an array with $2^d$ elements into a multidimensional $2\times \dots \times 2$ array and then applying tensor train (TT) decomposition is known under the name quantized TT decomposition (QTT).

It has been shown in a number of works that arrays arising in the discretization of certain PDEs allow QTT representation with a small number of parameters. However, the quest for robust and at the same time efficient QTT algorithm to solve PDEs with three (and more) physical dimensions is not over yet. In this talk, we address this problem using the example of PDEs arising in electronic structure calculation with a new algorithm, which is capable of solving PDEs discretized using $2^{100}$ grid points within minutes of computational time on a laptop.