  We generalize quantum circuits for the Toffoli gate presented by Selinger and
Jones for functionally controlled NOT gates, i.e., $X$ gates controlled by
arbitrary $n$-variable Boolean functions. Our constructions target the gate set
consisting of Clifford gates and single qubit rotations by arbitrary angles.
Our constructions use the Walsh-Hadamard spectrum of Boolean functions and
build on the work by Schuch and Siewert and Welch et al. We present quantum
circuits for the case where the target qubit is in an arbitrary state as well
as the special case where the target is in a known state. Additionally, we
present constructions that require no auxiliary qubits and constructions that
have a rotation depth of 1.
