A co-optimization qubit mapping algorithm via two-stage search and bidirectional look

Abstract Current quantum devices typically lack full qubit connectivity, making it difficult to directly execute logical circuits on quantum devices. This limitation necessitates quantum circuit mapping algorithms to insert SWAP gates, dynamically remapping logical qubits to physical qubits, and transforming logical circuits into physical circuits that comply with device connectivity constraints. However, the insertion of SWAP gates increases both the gate count and circuit depth, ultimately reducing the fidelity of quantum algorithms. To achieve a balanced optimization of these two objectives, we propose the TANGO algorithm. The algorithm first formulates an evaluation function that balances the impact of qubit mapping on both mapped and unmapped nodes is introduced to enhance initial mapping quality, thereby reducing the number of SWAP gates inserted during routing. Next, we design an innovative two-stage routing algorithm that prioritizes the number of executable gates as the primary evaluation metric while also considering quantum gate distance, circuit depth, {and a novel bidirectional-look SWAP strategy}, which optimizes SWAP gate selection in conjunction with preceding gates, improving the effectiveness of the mapping algorithm. Finally, by integrating advanced quantum gate optimization techniques, the algorithm's overall performance is further enhanced. Experimental results demonstrate that, compared to state-of-the-art methods, the proposed algorithm achieves multi-objective co-optimization of gate count and circuit depth across various benchmarks and quantum devices, exhibiting significant performance advantages.