It is well known that quantum algorithms may solve problems efficiently that are intractable using conventional algorithms. Quantum algorithms can be designed with a set of universal quantum gates that transform input states into desired output states. However, designing quantum algorithms that transform states in desired ways is challenging due to its complexity. In this paper, we propose a machine learning framework for the transformation of unknown states into their corresponding target states. Specifically, a parameterized quantum circuit learns a given task by tuning its parameters. After the learning is done, the circuit is competent for the quantum task. This allows us to circumvent cumbersome circuit design based on universal quantum gates. If perfect transformation is forbidden by quantum theory, an optimal transformation can be obtained in terms of fidelity. This provides a research method to study various quantum no-go theorems that characterize the intrinsic gap between quantum and classical information. As examples, quantum state rotation and quantum state cloning are studied using numerical simulations. We also show the good robustness of our machine learning framework to corrupted training data, which is a very nice property for physical implementation on near-term noisy intermediate-scale quantum devices.

众所周知，量子算法可以有效地解决使用传统算法难以解决的问题。可以使用一组通用量子门设计量子算法，将输入状态转换为所需的输出状态。然而，由于其复杂性，设计以所需方式转换状态的量子算法具有挑战性。在本文中，我们提出了一种机器学习框架，用于将未知状态转换为相应的目标状态。具体来说，参数化量子电路通过调整其参数来学习给定的任务。学习完成后，电路就可以胜任量子任务了。这使我们能够规避基于通用量子门的繁琐电路设计。如果量子理论禁止完美变换，可以在保真度方面获得最佳转换。这提供了一种研究方法来研究表征量子信息和经典信息之间的内在差距的各种量子不通过定理。例如，使用数值模拟研究量子态旋转和量子态克隆。我们还展示了我们的机器学习框架对损坏的训练数据的良好鲁棒性，这是在近期嘈杂的中尺度量子设备上物理实现的一个非常好的特性。