• This work proposes a practical initial layout method that utilizes matrix formulation to determine enhanced qubit assignments, without iterative optimization techniques and combinatorial search. • The proposed method computes the gradient of the objective function through a single matrix differentiation to obtain assignment suitability information between logical and physical qubits. • The gradient matrix encodes the interaction between physical-qubit centrality and logical-qubit connectivity, enabling direct mapping decisions that minimize error costs while satisfying hardware constraints. • Simulation results show that the proposed method improves computational efficiency while maintaining comparable execution reliability compared to existing qubit mapping methods. Qubit mapping is a crucial compilation process that assigns logical qubits from quantum circuits to physical qubits on quantum hardware, ensuring efficient and reliable execution on noisy intermediate-scale quantum (NISQ) computers. However, as the scale of quantum computers and circuit complexity increase, existing mapping approaches face significant computational complexity and suboptimal mapping quality. This work formulates the logic-to-physical qubit mapping problem as a matrix-form optimization problem to address scalability and computational efficiency challenges. The proposed method computes the gradient of the matrix-formulated problem through a single matrix differentiation and uses it as guidance to determine the enhanced qubit assignment, without the need for iterative combinatorial exploration and optimization solvers. Simulation results show that the proposed method achieves comparable execution reliability while significantly reducing the compilation time, even for multi-programming scenarios and large-scale quantum computers.
Piao et al. (Sun,) studied this question.