Théorique, numérique
Quantum computers are expected to change computations as we know it. How are they supposed to do that? Essentially they allow us to perform a subpart of linear algebra (certain matrix-vector multiplications) on exponentially large vectors. A natural mathematical famework to understand what they do is the tensor network formalism. Conversally, tensor networks are becoming popular as tools that can take the place of quantum computers, yet run on perfectly classical hardware. To do so, they rely on a hidden underlying structure of some mathematical problems (a form of intrication) that can be harvested to compress exponentially large vectors into small tensor networks. An increasing number of, apparently exponentially difficult, problems are getting solved this way. This internship lies at the intersection between theoretical quantum physics and applied mathematics. The goal will be to develop and apply new algorithms to “beat the curse of dimensionality”, i.e. to push the frontier of problems that we are able to access computationally. More specifically, we will explore a new approach to address a class of high dimensional integrals that arise in the context of Feynman diagram calculations [1]. The envisionned algorithms combine the normalization flow approach (from neural networks) with the tensor cross interpolation (from tensor networks). [1] https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.041038