  This paper explores artificial intelligence (AI) methods for the approximate
compiling of unitaries, focusing on the use of fixed two-qubit gates and
arbitrary single-qubit rotations typical in superconducting hardware. Our
approach involves three main stages: identifying an initial template that
approximates the target unitary, predicting initial parameters for this
template, and refining these parameters to maximize the fidelity of the
circuit. We propose AI-driven approaches for the first two stages, with a deep
learning model that suggests initial templates and an autoencoder-like model
that suggests parameter values, which are refined through gradient descent to
achieve the desired fidelity. We demonstrate the method on 2 and 3-qubit
unitaries, showcasing promising improvements over exhaustive search and random
parameter initialization. The results highlight the potential of AI to enhance
the transpiling process, supporting more efficient quantum computations on
current and future quantum hardware.
