Department of Physics • University of Cologne

Several lattice models display a condensation transition in real space when the density of a suitable order parameter exceeds a critical value. At equilibrium there are well established results and we discuss different scenarios of the condensation transition. In the out-of-equilibrium setup we consider one of such model with two conservation laws, attached to two external reservoirs, R_1 and R_2. Both reservoirs impose subcritical boundary conditions: When R_1=R_2 the system is in equilibrium below the localization threshold and no condensate appears. Instead, when R_1 differs from R_2 localization may arise in an internal portion of the lattice. This phenomenon is due to the coupled transport of two conserved quantities. In collaboration with Gabriele Gotti and Stefano Iubini.

There are few candidates for quantum algorithms which might outperform classical approaches while being amenable to noisy quantum computing devices. Beside quantum simulation algorithms, quantum algorithms for approximate optimization are promising candidates. The target application for these approaches is finding approximate solutions to combinatorial optimization problems. In this talk I will give an overview on quantum approximate optimization approaches, while mainly focusing on the quantum approximate optimization algorithm (QAOA), quantum annealing and variations thereof. I will demonstrate these concepts by considering a particular real-world planning problem, the flight-gate assignment problem [1]. In addition, I will cover novel approaches for the diagrammatic analysis of parametrized quantum circuits, like QAOA. Here I will demonstrate how such methods can be employed to help with the performance investigation of QAOA and other variational quantum algorithms. [1] https://ieeexplore.ieee.org/document/9222273 [2] https://arxiv.org/abs/2204.01307

Workshop MENTAL HEALTH IN MASTER/PHD STUDIES - CHALLENGES AND COPING STRATEGIE