  Quantum computing is regarded as a promising paradigm that may overcome the
current computational power bottlenecks in the post-Moore era. The increasing
maturity of quantum processors, especially superconducting ones, provides more
possibilities for the development and implementation of quantum algorithms. As
the crucial stages for quantum algorithm implementation, the logic circuit
design and quantum compiling have also received significant attention, which
covers key technologies such as quantum logic circuit synthesis (also widely
known as quantum architecture search) and optimization, as well as qubit
mapping and routing. Recent studies suggest that the scale and precision of
related algorithms are steadily increasing, especially with the integration of
artificial intelligence methods. In this survey, we systematically review and
summarize a vast body of literature, exploring the feasibility of an integrated
design and optimization scheme that spans from the algorithmic level to quantum
hardware, combining the steps of logic circuit design and compilation
optimization. Leveraging the exceptional cognitive and learning capabilities of
AI algorithms, one can reduce manual design costs, enhance the precision and
efficiency of execution, and facilitate the implementation and validation of
the superiority of quantum algorithms on hardware.
