Classification of Hybrid Quantum-Classical Computing

As quantum computers mature, the applicability in practice becomes more important. Quantum computers will often be used in a hybrid setting, where classical computers still play an important role in operating and using the quantum computer. However the term hybrid is diffuse and multi-interpretable. In this work we define two classes of hybrid quantum-classical computing: vertical and horizontal hybrid quantum-classical computing. The first is application-agnostic and concerns using and operating 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 introduce terms for them