Project Title: Constrained Optimization with Low-Rank Tensor ApproximationsAdvisors: F. Oztoprak Topkaya (Artelys), M. Gabay (Artelys), B. Mourrain (Inria), C. Riener (UiT) Mentor: A. Mantzaflaris (Inria) Objectives: In certain applications, the desired solution of an optimization problem can be stated as a tensor. Typically, the size of such a tensor grows…
Project Title: Tensor and polynomial optimisation for quantum information networksAdvisors: A. Acin (ICFO), V. Magron (LAAS) Mentor: S. Mansfield (Quandela) Objectives: We consider quantum communication systems with network of users, corresponding to a network of Hilbert space tensor products, which raises important computational challenges. Different type of correlations will be…
Project Title: State preparation of matrix-product operationsAdvisors: J. Marecek (CTU) , D. Henrion (LAAS), M. Korda (LAAS) Mentor: G. Korpas (HSBC Lab) Objectives: Many practical quantum circuits operate with multiple quantum registers, storing multiple types of input, some ancillas, and some output registers. In the corresponding initial state preparation, one…
Project Title: Approximation hierarchies for quantum entanglement detectionAdvisors: M. Laurent (NWO-I), V. Magron (CNRS), Mentor: M. Almeida (Quantinuum) Objectives: Tensor products model quantum state systems consisting of multiple subsystems. Detecting whether a quantum state is entangled (or separable) is a fundamental question in quantum information theory, which boils down to…
Project Title: Geometry of Hermitian tensor spacesAdvisors: G. Ottaviani (UniFI), Yang Qi (Inria), B. Mourrain (Inria) Mentor: E. Rubei (UniFI) Objectives: Tensor spaces have natural distances invariant under the orthogonal group or the unitary group, respectively in the real or the complex setting. Several optimisation problems in tensor spaces consist…
Project Title: Geometry of tensor network varieties for quantum condensed matter physicAdvisors: I. Carusotto (INO-BEC, CNR), S. Telen (MPG) Mentor: S. Mansfield (Quandela) Objectives: Tensor Networks (TN) are a convenient way to represent those strongly entangled quantum states that appear in interacting many-particle systems and compute their physical properties. The…
Project Title: Algorithms for Tensor DecompositionAdvisors: A. Bernardi (UniTN), A. Oneto (UniTN), B. Mourrain (Inria) Mentor: Federico Lucca (BlueTensor) Objectives: The objective of the project is from the academic side it intends to investigate and develop new methods and algorithms for tensor decomposition (TD), and from the industrial side the…
Project Title: Tensor optimization for storage integrationAdvisors: C. Bordin (UiT), C. Riener (UiT), M. Schweighofer (UKON), Mentors: Julien Moisan (Arva), Sigurd Bakkejord (Arva), Inga Setsa Holmstrand (Arva). Objectives: Optimal integration of storage in power and energy networks with a high share of intermittent renewable energy sources is one of the…
Project Title: Tensor decomposition with group invarianceAdvisors: H. Munthe-Kaas (UiT), C. Riener (UiT), E. Hubert (Inria), Mentor: Florian Strohl (UiT) Objectives: The so called orbit recovery problem is the problem of recovering a planted signal from noisy measurements under unknown group actions. More concretely, one tries to recover the unknown…
Project Title: Gibbs manifolds and semidefinite programmingAdvisors: B. Sturmfels (MPG), S. Telen (MPG), M. Laurent (NWO-I), Mentor: Georgios Korpas (HSBC) Objectives: Interior point methods for linear programming use regularization to reduce the problem to smooth convex optimisation on a polytope. A popular choice for the regularization is a strictly convex…
