Quantum technologies, i.e., technologies benefiting from the features of quantum physics such as objective randomness, superposition, and entanglement, have enabled an entirely different way of distributing and processing information. The enormous progress over the last decades has also led to an urgent need for young professionals and new educational programs. However, the lack of intuitive analogies and the necessity of complex mathematical frameworks often hinder teaching and learning efforts. Thus, novel education methods, such as those involving gamification, are promising supplements to traditional teaching methods. Here, we present a strategic card game in which the building blocks of a quantum computer can be experienced. While playing, participants start with the lowest quantum state, play cards to "program" a quantum computer, and aim to achieve the highest possible quantum state. By extending the game to high-dimensional quantum systems, i.e., systems that can take more than two possible values, and by developing different multi-player modes, the game can be used as an introduction to quantum computational tasks for students. As such, it can also be used in a classroom environment to increase the conceptual understanding, interest, and motivation of a student. Therefore, the presented game contributes to the ongoing efforts on gamifying quantum physics education with a particular focus on the counter-intuitive features which quantum computing is based on.