  A quantum circuit transformation (QCT) is required when executing a quantum
program in a real quantum processing unit (QPU). Through inserting auxiliary
SWAP gates, a QCT algorithm transforms a quantum circuit to one that satisfies
the connectivity constraint imposed by the QPU. Due to the non-negligible gate
error and the limited qubit coherence time of the QPU, QCT algorithms which
minimize gate number or circuit depth or maximize the fidelity of output
circuits are in urgent need. Unfortunately, finding optimized transformations
often involves exhaustive searches, which are extremely time-consuming and not
practical for most circuits. In this paper, we propose a framework that uses a
policy artificial neural network (ANN) trained by supervised learning on
shallow circuits to help existing QCT algorithms select the most promising SWAP
gate. ANNs can be trained off-line in a distributed way. The trained ANN can be
easily incorporated into QCT algorithms without bringing too much overhead in
time complexity. Exemplary embeddings of the trained ANNs into target QCT
algorithms demonstrate that the transformation performance can be consistently
improved on QPUs with various connectivity structures and random or realistic
quantum circuits.
