In recent years, quantum computing has become popular due to its potential ability to solve problems that are beyond the possibilities of classical computing infrastructures. Although the status of quantum devices is still in its early stage, there are many theoretical quantum algorithms already available. The examples include not only the famous polynomial time Shor factorization but also the new hybrid classical-quantum approach used for optimisation. In this talk, we present an introduction to quantum algorithms and the current status of publicly available quantum hardware. We also give an overview of the research conducted in the Institute of Computer Science AGH including optimisation of workflow scheduling as well as  EU projects EuroHPC and Lumi-Q run at ACK Cyfronet AGH related to quantum topics.