This paper provides an overview of quantum circuit synthesis and compilation optimization, highlighting the challenges and advancements in the field. Quantum computing is seen as a promising solution to overcome computational power bottlenecks, with the increasing maturity of quantum processors, particularly superconducting ones, driving the development and implementation of quantum algorithms. The paper discusses key technologies such as quantum logic circuit synthesis (also known as quantum architecture search), optimization, qubit mapping, and routing. It reviews recent studies that integrate artificial intelligence methods to enhance the scale and precision of these algorithms. The authors 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. They emphasize the importance of leveraging AI algorithms to reduce manual design costs, enhance precision and efficiency, and facilitate the implementation and validation of quantum algorithms on hardware. The paper also delves into the representation of quantum circuits, including the quantum gate model, directed acyclic graphs (DAGs), phase polynomials, tensor networks, and ZX diagrams. These representations are crucial for synthesis and optimization methods, which aim to transform quantum algorithms into executable quantum programs. The authors discuss various methods for quantum circuit synthesis, such as heuristic algorithms (e.g., genetic algorithms, simulated annealing), reinforcement learning, and sampling-based learning algorithms. They analyze the strengths and limitations of each approach and propose an integrated solution that combines these methods to address the challenges of quantum circuit design and compilation. Finally, the paper discusses the optimization of quantum circuits, focusing on balancing theoretical accuracy and practical noise. It explores different optimization objectives and methods, including pattern matching, peephole optimization, and machine learning approaches. The authors also address the compilation process, which involves mapping logical qubits to physical qubits and adding necessary SWAP gates to ensure circuit connectivity. The contributions of the paper include a comprehensive analysis of the steps and challenges in quantum algorithm development and execution, a systematic organization of algorithms and their characteristics, and the proposal of an integrated quantum circuit design and compilation solution that leverages AI to enhance performance and design efficiency.This paper provides an overview of quantum circuit synthesis and compilation optimization, highlighting the challenges and advancements in the field. Quantum computing is seen as a promising solution to overcome computational power bottlenecks, with the increasing maturity of quantum processors, particularly superconducting ones, driving the development and implementation of quantum algorithms. The paper discusses key technologies such as quantum logic circuit synthesis (also known as quantum architecture search), optimization, qubit mapping, and routing. It reviews recent studies that integrate artificial intelligence methods to enhance the scale and precision of these algorithms. The authors 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. They emphasize the importance of leveraging AI algorithms to reduce manual design costs, enhance precision and efficiency, and facilitate the implementation and validation of quantum algorithms on hardware. The paper also delves into the representation of quantum circuits, including the quantum gate model, directed acyclic graphs (DAGs), phase polynomials, tensor networks, and ZX diagrams. These representations are crucial for synthesis and optimization methods, which aim to transform quantum algorithms into executable quantum programs. The authors discuss various methods for quantum circuit synthesis, such as heuristic algorithms (e.g., genetic algorithms, simulated annealing), reinforcement learning, and sampling-based learning algorithms. They analyze the strengths and limitations of each approach and propose an integrated solution that combines these methods to address the challenges of quantum circuit design and compilation. Finally, the paper discusses the optimization of quantum circuits, focusing on balancing theoretical accuracy and practical noise. It explores different optimization objectives and methods, including pattern matching, peephole optimization, and machine learning approaches. The authors also address the compilation process, which involves mapping logical qubits to physical qubits and adding necessary SWAP gates to ensure circuit connectivity. The contributions of the paper include a comprehensive analysis of the steps and challenges in quantum algorithm development and execution, a systematic organization of algorithms and their characteristics, and the proposal of an integrated quantum circuit design and compilation solution that leverages AI to enhance performance and design efficiency.