IQIM Postdoctoral and Graduate Student Seminar

Joint IQIM/AWS Seminar

Abstract: The notorious "exponential scaling wall" in quantum mechanics is defined as exponential growth of the simulation complexity with the number of particles in the system. As applied to chemical systems, this problem appears in electronic structure theory (for electrons) and magnetic resonance (for electron and nuclear spin). Multi-electron systems in chemistry have a notion of distance and well-defined ground states; this leads to many excellent approximations with linear complexity scaling. However, spin systems have neither, and simulation of multi-spin dynamics is, even at present, a difficult problem. The natural structure of quantum mechanical Hamiltonians for many-body systems is a large sum of Kronecker products of very small matrices. A very promising recent class of approximations broadly revolves around the idea of never opening those Kronecker products. These approximations are variously known as DMRG (density matrix renormalisation group), MPS (matrix product states), TT (tensor trains) and, in general "tensor network methods". This seminar is about our experience using tensor network approximations in magnetic resonance spectroscopy and imaging. To summarise a very long story: yes, they work – but you will need to rewrite the entire formalism of your subject around tensor networks to make that happen

Attend by zoom at https://caltech.zoom.us/j/88407627311?pwd=RGx4MlpSUnBLbDJvdE4rS1FHbWZvUT09