As the leading candidate for quantum error correction, the surface code faces substantial overhead, such as redundant physical qubits and prolonged execution time. Reducing the space-time cost of circuit execution can significantly improve the throughput of modern quantum cloud platforms. While utilizing more physical qubits can reduce execution time, different quantum circuits vary in their ability to leverage chip resources. Therefore, optimizing the compilation of surface code circuits on quantum chips becomes critical. In this work, we address the mapping and scheduling problem in compiling surface code to reduce the cost. First, we introduce a novel metric Circuit Parallelism Degree to characterize circuit properties in detail and select the most suitable chip from a list of available options. Next, we will quantitatively assess the resources to determine if they are sufficient for the circuit. We then propose a resource-adaptive mapping and scheduling method called Ecmas+ , which customizes the initialization of chip resources for each circuit. Ecmas+ significantly reduces execution time in the double defect and lattice surgery models. Extensive numerical tests on practical datasets demonstrate that Ecmas+ outperforms state-of-the-art methods, reducing execution time by an average of 46% for the double defect model and 29.7% for the lattice surgery model.

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$2+ {+}$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$22.3\times $, with an average increase of$6.1\times $. Concurrently, it maintains the effectiveness of the transformed circuit depth.

As the leading candidate of quantum error correction codes, surface code suffers from significant overhead, such as execution time. Reducing the circuit's execution time not only enhances its execution efficiency but also improves fidelity. However, finding the shortest execution time is NP-hard. In this work, we study the surface code mapping and scheduling problem. To reduce the execution time of a quantum circuit, we first introduce two novel metrics: Circuit Parallelism Degree and Chip Communication Capacity to quantitatively characterize quantum circuits and chips. Then, we propose a resource-adaptive mapping and scheduling method, named Ecmas, with customized initialization of chip resources for each circuit. Ecmas can dramatically reduce the execution time in both double defect and lattice surgery models. Furthermore, we provide an additional version Ecmas-ReSu for sufficient qubits, which is performance-guaranteed and more efficient. Extensive numerical tests on practical datasets show that Ecmas outperforms the state-of-the-art methods by reducing the execution time by 51.5 % on average for double defect model. Ecmas can reach the optimal result in most benchmarks, reducing the execution time by up to 13.9 % for lattice surgery model.

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. 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.