Many circuit-based quantum programming languages contain limited functionality for handling programs with quantum branching events. In this paper we introduce a hierarchical circuit language with two new connectives, one for generalized controlled operations and one for sub-circuit exponentiation, to reason formally about such programs. We construct the hierarchical circuit language using a novel category-theoretic construction, demonstrate that its compositional properties are non-trivial, show a circuit identity which may be useful for circuit optimization by a compiler, demonstrate how generalized controlled operations describe quantum control flow, and then contrast generalized controlled operations with Pauli rotations.