Kareem Diab

Exploring whether QSVT might be used to implement spectral methods for graph problems, such as community detection or graph partitioning,

Investigating how symmetry problems—including graph isomorphism variants—may be expressed as nonlocal games, and how NPA/SoS relaxations provide insight into entanglement structure and quantum–classical separations.

I was studying navigation functions on configuration spaces for robot motion planning and thought about how similar ideas could be applied to variational quantum algorithms. Thinking about the energy landscape of particularly complex optimization problems with several local minima got me thinking about the complex low energy states of NLTS-type Hamiltonians, and whether similar insights could be used to understand these hamiltonians and the preparation of their low energy states.