  Predicting the optimum SWAP depth of a quantum circuit is useful because it
informs the compiler about the amount of necessary optimization. Fast
prediction methods will prove essential to the compilation of practical quantum
circuits. In this paper, we propose that quantum circuits can be modeled as
queuing networks, enabling efficient extraction of the parallelism and duration
of SWAP circuits. To provide preliminary substantiation of this approach, we
compile a quantum multiplier circuit and use a queuing network model to
accurately determine the quantum circuit parallelism and duration. Our method
is scalable and has the potential speed and precision necessary for large scale
quantum circuit compilation.
