Quantum computers have the potential to bring forth a major breakthrough in scientific computing. The foreseen increase in computational efficiency offered by quantum computing is of such magnitude that, despite being in its infancy, it is already being coupled with traditional high-performance computing technology. Here, we give an overview of quantum computing, the present state of affairs, and future scenarios. Europe has a unique opportunity to create world-leading supercomputing infrastructures incorporating quantum technology, by capitalising on the established expertise of European HPC centres in conjunction with the emerging European quantum ecosystem. This requires dedicated and sustained funding for quantum hardware and software developments, as well as for education. In addition, coordinated efforts and support for early adoption of quantum computing in academia and industry are essential.