Description
This research proposal focuses on the development of novel algorithms and use case applications of Tensor Networks (TNs), a new and extremely powerful framework providing a way to systematically perform controlled truncations of high-dimensional linear algebra problems. This represents a formidable tool, which has allowed to study with unprecedented accuracy a wide variety of quantum manybody systems, a task which, if performed with traditional methods, would involve an exponential cost in computational resources as the number of constituents of the system grows.
We plan to pioneer applications of TNs to new areas of physics, both fundamental and applied, exploiting their expressivity and efficiency. Our focus will be on three main directions: the use of TNs to solve differential equations, such as those of fluid dynamics, the study of time evolution of quantum systems, and the pioneering of applications of TNs for high-energy physics. For this, we will design novel algorithms tailored to these new challenges, paving the way to novel results and improving performance and accuracy beyond current state-of-the-art methods. We will implement these new algorithms in a public software library targeted at high performance parallel environments, such as the MareNostrum cluster installed at the Barcelona Supercomputing Center (BSC). We thus aim at both advancing fundamental research, as well as providing novel tools for academia and possible industrial partners, in an open format.
