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.

翻译：由于量子计算资源的稀缺性，研究人员和开发者对真实量子计算机的访问权限非常有限。因此，明智地规划和利用量子计算机的运行时间对于确保项目顺利执行和完成至关重要。准确估计量子程序的执行时间，可以防止意外超出预期运行时间或量子计算机的最大容量；同时也使得量子计算平台能够基于精确信息来配置和优先处理量子计算任务。本文首先研究了量子程序在模拟器和真实量子计算机上的运行时间特征。随后，我们引入了一种创新方法，该方法采用基于图Transformer的模型，利用量子程序的图信息和全局信息来估计其执行时间。我们选取了一个包含超过1510个量子程序的基准数据集，首先预测了它们在模拟器上的执行时间，取得了令人满意的结果，其R平方值超过95%。接着，对于量子计算机上的执行时间估计，我们应用主动学习方法，以95%的置信度选取了340个样本来构建和评估我们的方法，实现了平均R平方值超过90%的成果。我们的方法可以集成到量子计算平台中，以提供对量子执行时间的准确估计，并作为优先处理量子执行任务的参考依据。此外，我们的研究结果为量子程序开发者在优化程序执行时间消耗方面提供了见解，例如，优先使用单量子比特门而非双量子比特门。