In the talk I summarize briefly the state of the art of QUBO (Quadratic Unconstrained Binary Optimization) models. The summary will include an overview of the most important results in classical operations research, the recent achievements of classical solver development, a subjective view on the quantum line, especially concerning DWave. I also summarize briefly the results achieved during the collaboration between groups at IITiS PAN and at Wigner Research Centre for Physics, and presented some of the plans for the near future.

The seminar will include the second part of a lecture on classical and quantum automata. After having a few examples on the DFAs with discussions on their limitations, we introduce their probabilistic and quantum variants. We present a representative algorithm for each of these variants, followed by a discussion on the quantum advantages in finite automata settings. We shortly review the recent implementations of QFA algorithms on real quantum hardware.