Due to the scarcity of quantum computing resources, researchers and developers have very limited access to real quantum computers. Therefore, judicious planning and utilization of quantum computer runtime are essential to ensure smooth execution and completion of projects. Accurate estimation of a quantum program's execution time is thus necessary to prevent unexpectedly exceeding the anticipated runtime or the maximum capacity of the quantum computers; it also allows quantum computing platforms to make precisely informed provisioning and prioritization of quantum computing jobs. In this paper, we first study the characteristics of quantum programs' runtime on simulators and real quantum computers. Then, we introduce an innovative method that employs a graph transformer-based model, utilizing the graph information and global information of quantum programs to estimate their execution time. We selected a benchmark dataset comprising over 1510 quantum programs, initially predicting their execution times on simulators, which yielded promising results with an R-squared value over 95%. Subsequently, for the estimation of execution times on quantum computers, we applied active learning to select 340 samples with a confidence level of 95% to build and evaluate our approach, achieving an average R-squared value exceeding 90%. Our approach can be integrated into quantum computing platforms to provide an accurate estimation of quantum execution time and be used as a reference for prioritizing quantum execution jobs. In addition, our findings provide insights for quantum program developers to optimize their programs in terms of execution time consumption, for example, by prioritizing one-qubit gates over two-qubit gates.

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