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：量子过程学习正成为研究量子系统的重要工具。尽管在相干框架（目标系统与模型系统可共享量子信息）中已得到广泛研究，但关于无需系统与目标直接交互即可学习量子系统动力学的问题受到的关注较少。此类非相干框架具有实际吸引力，因为它们为不同物理平台间的量子过程转译开辟了新途径，无需依赖技术上具有挑战性的混合纠缠方案。本文通过分析模拟成熟相干学习策略所需的测量次数，给出了非相干学习酉过程样本复杂度的界。我们证明：若允许任意测量，则任何高效可表示的酉算符均可通过非相干框架高效学习；但当仅允许浅层测量时，仅能学习低纠缠酉算符。我们通过成功在\texttt{ibmq\_kolkata}上学习16量子比特酉算符，展示了针对低纠缠酉算符的非相干学习算法，并基于大量数值实验进一步验证了所提算法的可扩展性。