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As the leading candidate of quantum error correction codes, surface codesuffers from significant overhead, such as execution time. Reducing thecircuit's execution time not only enhances its execution efficiency but alsoimproves fidelity. However, finding the shortest execution time is NP-hard.  In this work, we study the surface code mapping and scheduling problem. Toreduce the execution time of a quantum circuit, we first introduce two novelmetrics: Circuit Parallelism Degree and Chip Communication Capacity toquantitatively characterize quantum circuits and chips. Then, we propose aresource-adaptive mapping and scheduling method, named Ecmas, with customizedinitialization of chip resources for each circuit. Ecmas can dramaticallyreduce 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 testson practical datasets show that Ecmas outperforms the state-of-the-art methodsby reducing the execution time by 51.5% on average for double defect model.Ecmas can reach the optimal result in most benchmarks, reducing the executiontime by up to 13.9% for lattice surgery model.

Ecmas: Efficient Circuit Mapping and Scheduling for Surface Code