In this talk I will describe the state of the art in higher-order quantum computation. To place things in context, I will briefly present you the two main paradigms in which research is being done: quantum control and classical control. We will then focus on the later, the most understood one. In this setting, we have to deal with quantum (non-duplicable) and classical (duplicable) data, higher-order structures, and a probabilistic side-effect. We will analyze an abstract machine and explore the denotational tools that are useful for getting some insights on this computational paradigm.