  We introduce the PBS-calculus to represent and reason on quantum computations
involving coherent control of quantum operations. Coherent control, and in
particular indefinite causal order, is known to enable multiple computational
and communication advantages over classically ordered models like quantum
circuits. The PBS-calculus is inspired by quantum optics, in particular the
polarising beam splitter (PBS for short). We formalise the syntax and the
semantics of the PBS-diagrams, and we equip the language with an equational
theory, which is proved to be sound and complete: two diagrams are representing
the same quantum evolution if and only if one can be transformed into the other
using the rules of the PBS-calculus. Moreover, we show that the equational
theory is minimal. Finally, we consider applications like the implementation of
controlled permutations and the unrolling of loops.
