### Dmitry Savostyanov (Institute of Numerical Mathematics, RAS, Moscow and University of Chester)

#### Tensor trains and quantum algorithms: impossible is possible

*Wednesday 7 December 2011 at 15.30, JCMB 6206*

##### Abstract

This talk is largely concerned with tensor trains. This recent format allows
nice and simple data-sparse representation for both the high- and
low-dimensional data, based on the separation of indices and tensor product
representation. The algebraic techniques and comprehensive error analysis
behind the tensor train computations make it possible to develop a full set of
linear algebra subroutines to perform the computations with huge arrays given
in the compact data-sparse format. The most impressive results of the tensor
trains is the possibility to overcome the curse of dimensionality for the
solution of high-dimensional problems and to build up the effective classical
models of the quantum algorithms, which were considered as impossible task
several years ago. However, a lot of effort is still need to be invested to
establish and describe the class of problems for which the use of tensor
trains is effective and to develop the rigorous convergence analysis for the
algorithms based on tensor train representations.