Effective and Efficient Parallel Qubit Mapper

Quantum computing has been accumulating tremendous attention in recent years. In current superconducting quantum processors, each qubit can only be connected with a limited number of neighbors. Therefore, the original quantum circuit should be converted to a hardware-dependent circuit, and this process is called qubit mapping and routing, in which typically extra SWAP gates need to be inserted. Due to a limited qubit lifetime, one of the main objectives of qubit mapping and routing is to minimize the circuit depth, which is a time-consuming process. By studying several existing greedy mappers, we extract and analyze two patterns that significantly impact the mapping and routing performance. Then, we propose a sliding window method named SWin, which dramatically reduces the computational cost with negligible performance degradation. For devices with constrained executable circuit depth, we propose SWin+, which introduces adaptive circuit slicing methods with VF<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2+ {+}$ </tex-math></inline-formula> subgraph isomorphism initial mapping methods. Compared with the state-of-the-art greedy methods, SWin can find an effective result by up to 39% depth decrease, on average of 16% for large-scale circuits. Moreover, SWin can be easily modified to be noise-aware, while the depth reduction will yield better performance for real execution. Furthermore, SWin still performs well for various chip couplings. SWin+ significantly enhances processing efficiency, achieving improvements up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$22.3\times $ </tex-math></inline-formula>, with an average increase of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.1\times $ </tex-math></inline-formula>. Concurrently, it maintains the effectiveness of the transformed circuit depth.