The establishment of digital humanities as a research field has shown that the use of computers as tools, but also the use of methods and techniques from computer science, can contribute enormously to research done in the humanities. Since quantum computers are expected to become generally available in the next few years, it is promising to use the advantages of this new technology for addressing existing as well as completely new questions in the humanities. The use of quantum computers offers a great deal of potential: (i) they are much faster than classical computers in solving certain complex problems, (ii) solutions may be much more precise, (iii) they allow the solution of problem classes that can hardly been solved on classical computers, and (iv) their usage promises to be much cheaper than that of supercomputers. Parts of this potential are already used in different domains but are also particular promising for digital humanities research. This paper outlines the vision of such quantum humanities.