Quantum process learning is emerging as an important tool to study quantum systems. While studied extensively in coherent frameworks, where the target and model system can share quantum information, less attention has been paid to whether the dynamics of quantum systems can be learned without the system and target directly interacting. Such incoherent frameworks are practically appealing since they open up methods of transpiling quantum processes between the different physical platforms without the need for technically challenging hybrid entanglement schemes. Here we provide bounds on the sample complexity of learning unitary processes incoherently by analyzing the number of measurements that are required to emulate well-established coherent learning strategies. We prove that if arbitrary measurements are allowed, then any efficiently representable unitary can be efficiently learned within the incoherent framework; however, when restricted to shallow-depth measurements only low-entangling unitaries can be learned. We demonstrate our incoherent learning algorithm for low entangling unitaries by successfully learning a 16-qubit unitary on \texttt{ibmq\_kolkata}, and further demonstrate the scalabilty of our proposed algorithm through extensive numerical experiments.
翻译:量子进程学习是研究量子系统的重要工具。虽然在共振框架中得到了广泛研究,其中目标和模型系统可以共享量子信息,但较少关注的是是否可以在系统和目标直接交互的情况下学习量子系统的动力学。这种不连贯的框架在实践中极具吸引力,因为它打开了在不需要具有技术上具有挑战性的混合纠缠方案的情况下,在不同物理平台之间传输量子进程的方法。在本文中,通过分析需要模拟已建立的连贯学习策略的测量次数,提供了在不连贯框架下学习单元过程的样本复杂度界限。我们证明,如果允许任意测量,则可以在不相互耦合的框架内有效地学习任何有效代表单元,但当限制为浅层测量时,只能学习低耦合单元。我们通过成功在\texttt{ibmq\_kolkata}上学习16个量子位单元的不连贯学习算法,并通过广泛的数值实验进一步证明了我们提出的算法的可扩展性。