Delft Institute of Applied Mathematics
Aad van der Vaart wordt President van de International Society for Bayesian AnalysisAad van der Vaart is gekozen tot President Elect van de International Society for Bayesian Analysis (ISBA). Zijn termijn begint op 1 januari 2023 en een jaar later zal hij het voorzitterschap van de Society overnemen.
22 maart 2023 14:00 t/m 15:00
[DMO] Barbara Terhal & Maarten Stroeks: Fermionic OptimizationA basic problem in physics is to determine the lowest eigenvalue, or `ground state energy', of a many-body Hamiltonian. For fermionic Hamiltonians, modeling electrons in solids or chemistry, this problem is the minimization of a low-degree polynomial in non-commutative Majorana variables (forming a Clifford algebra). Since determining the lowest eigenvalue is a (QMA)-hard problem, it has been of interest to upper and lower bound the eigenvalue by optimizing over simple classes of states resp. relaxing the problem to a SDP.
We prove that for sparse fermionic Hamiltonians the upperbound over so-called Gaussian fermionic states, a well-known efficiently described class of quantum states, achieves a constant approximation ratio, meaning that the scaling with the number of variables is the same as for the true lowest eigenvalue. This is in contrast to recent work showing that for a class of random dense fermionic Hamiltonians, with high probability, there is no constant approximation ratio. We discuss some further results and open questions in this area.
References: 1. Herasymenko, Stroeks, Helsen, Terhal, https://arxiv.org/abs/2211.16518 ; 2. Hastings, O'Donnell, https://dl.acm.org/doi/10.1145/3519935.3519960
We focus on Functional Analysis and Operator Theory with applications to the study of (partial) differential equations, both deterministic and non-deterministic.
We cover a large spectrum of research areas in probability theory, going from very application-driven towards fundamental research.
Discrete Mathematics & Optimization
Mathematical optimization lies at the heart of many techniques in economy, econometrics, process control, and so on.
We work on mathematical modeling of physical phenomena, often leading to systems of (partial) differential equations.
Our research program concentrates on the development and application of computing methods to the applied sciences.