Classification of Hybrid Quantum-Classical Computing

As quantum computers mature, the applicability in practice becomes more important. Many uses of quantum computers will be hybrid, with classical computers still playing an important role in operating and using the quantum computer. The term hybrid is however diffuse and multi-interpretable. In this work we define two classes of hybrid quantum-classical computing: vertical and horizontal. The first is application-agnostic and concerns using quantum computers. The second is application-specific and concerns running an algorithm. For both, we give a further subdivision in different types of hybrid quantum-classical computing and we coin terms for them.