Ecmas+: Efficient Circuit Mapping and Scheduling for Surface Code Encoded Circuit on Quantum Cloud Platform

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.