Quantum technologies have the potential to revolutionise the IT, pharmacy, chemistry, and energy sectors. The involvement of Widening Countries in the development of emerging technologies can narrow the gap with more advanced EU members and enhance overall innovation in the high-tech industry. Poland, equipped with significant expertise in theoretical physics, a substantial pool of top-tier information technology professionals, and advanced high-performance computing infrastructure, strategically aligns with these initiatives. However, the development of Quantum Technology faces substantial barriers. Due to the intricate nature of quantum processes, quantum states are often very fragile, and designing useful devices requires modelling with advanced theoretical and numerical tools. There is also a barrier on the theory side: despite potentially groundbreaking ideas, many concepts remain unexplored due to the absence of suitable modelling methods to demonstrate their applicability potential. The Modelling Center for Quantum Technologies group at the Center for Theoretical Physics PAS, Poland, aims to bridge the theory-experiment gap by developing and applying new methods to describe open quantum many-body systems comprehensively. Additionally, it will address the academia-business gap by establishing an open-source-based quantum modelling centre and fostering connections with research and industry partners through various dissemination and exploitation measures. With the expertise, networking capabilities, and strong commitment of the ERA Chair holder, this group of excellence strives to become a world leader in quantum system modelling, unlocking the full potential of theoretical research at the Center for Theoretical Physics PAS.