Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects

TL;DR

The paper tackles the challenge of turning quantum algorithms into executable programs by proposing an integrated, AI-driven workflow that spans quantum logic circuit synthesis, optimization, and compiling. It surveys multiple circuit representations (gate model, DAGs, phase polynomials, tensor networks, ZX diagrams) and how they support diverse synthesis and optimization tasks. It reviews Quantum Architecture Search (QAS) methods—heuristic, reinforcement learning, sampling-based, and differentiable/diffusion-based—and their applications with and without explicit target unitaries, including VQE, QNNs, QAOA, and error-correction codes. It then整理s optimization targets (gate/CNOT/T counts, depth, and T-depth) and corresponding techniques (BFS, pattern matching, reductions, ML) and discusses qubit mapping/routing as a critical compilation stage, all with attention to NISQ and FTQC constraints. The authors argue for a holistic, end-to-end AI-driven quantum compiler that leverages hardware calibration data and cloud platforms to automate design and optimization, enabling scalable, robust deployment of quantum algorithms.

Abstract

Quantum computing is a promising paradigm that may overcome the current computational power bottlenecks. The increasing maturity of quantum processors 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, e.g., 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, it becomes more possible to 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.

Figures (3)

• Figure 1: Quantum algorithm implementation pipeline. A quantum algorithm can be written in the form of multiple unitary transformations. logic circuit synthesis and optimization methods are then applied to obtain logic circuits. We utilize qubit mapping and routing methods to build an executable program during the quantum compiling stage. In this paper, we mainly focus on logic circuit design and quantum compiling.
• Figure 2: Quantum Circuit Representation. Gate Model: a popular representation method; DAG: example DAG transformed from the gate model example, "start" and "end" nodes are added to complete the graph; QMDD: QMDD representation of a three-qubit quantum operation; we present the transformation matrix, the layerwise structure and the size of the corresponding matrix of each node; Tensor Network: a quantum state $\ket{\psi}$ can be represented by multiple common types of tensor network; ZX-Diagram: the green and red spider in ZX-diagram as well as an example ZX-diagram transformed from gate model example.
• Figure 3: Quantum Circuit Compiling. (a) An example qubit topology of a superconducting quantum processor, we select four working qubits (marked as grey); (b) Logical circuit; (c) After mapping logical qubits $q_0,q_1,q_2,q_3$ to physical qubits $Q_9,Q_6,Q_{10},Q_{14}$, three SWAP gates are inserted since only neighbor qubits are connected; (d) Circuit after qubit routing which reduce the number of SWAP gates to only one.