  Variational quantum compiling algorithms \cite{qaqc} aim to compress quantum
circuits into parameterized ansatzes utilizing a hybrid quantum-classical
approach. In this article a variant of VQC named the recursive variational
quantum compiling algorithm (RVQC) is proposed. In contrast with existing VQC
algorithms, where one is required to execute the full target circuit in order
to compile it, RVQC works by dividing the target circuit into $N$ parts and
recursively compresses one part at a time into the parameterized ansatz. Since
smaller parts are being compressed at a time, the circuit depth required to
implement the algorithm is not dependent on the depth of the target circuit,
but on the depth of the ansatz and the depth of each of the $N$ parts. We are
hence able to compress the target circuit by executing circuits of smaller
depths than the target circuit itself. To show that this approach has an edge
over the standard VQC method for sufficiently large circuit depths, RVQC was
compared with VQC on a noise model of the IBM Santiago device with the goal of
compressing a randomly generated five-qubit circuit of depth 5000. It was shown
that VQC was not able to converge within 500 epochs of training. On the other
hand, RVQC was able to converge to a fidelity ($0.88$) within a total of 500
epochs when splitting the target circuit into $N = 5$ parts.
