An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task as represented by supervised learning with classical data. However, the provable advantages of QML in supervised learning have been known so far only for the learning tasks designed for using the advantage of specific quantum algorithms, i.e., Shor's algorithms. Here we explicitly construct an unprecedentedly broader family of supervised learning tasks with classical data to offer the provable advantage of QML based on general quantum computational advantages, progressing beyond Shor's algorithms. Our learning task is feasibly achievable by executing a general class of functions that can be computed efficiently in polynomial time for a large fraction of inputs by arbitrary quantum algorithms but not by any classical algorithm. We prove the hardness of achieving this learning task for any possible polynomial-time classical learning method. We also clarify protocols for preparing the classical data to demonstrate this learning task in experiments. These results open routes to exploit a variety of quantum advantages in computing functions for the experimental demonstration of the advantage of QML.

翻译：量子机器学习（QML）的一个总体里程碑是证明QML在所有可能的经典学习方法中具有优势，能够加速以经典数据监督学习为代表的常见学习任务。然而，迄今为止，QML在监督学习中的可证明优势仅针对为利用特定量子算法（即Shor算法）优势而设计的学习任务。本文明确构建了一个前所未有更广泛的监督学习任务族，基于通用量子计算优势提供QML的可证明优势，超越了Shor算法。我们的学习任务可通过执行一类通用函数可行地实现，这些函数对于大比例输入可由任意量子算法在多项式时间内高效计算，但任何经典算法都无法做到。我们证明了任何多项式时间的经典学习方法都无法实现这一学习任务。我们还阐明了制备经典数据以在实验中演示该学习任务的协议。这些结果为利用多种量子优势计算函数以实验证明QML优势开辟了途径。