Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process, under the assumption that the process has bounded information loss and induces causal dependencies whose strength is above a fixed (but otherwise arbitrary) threshold. Our method is based on a quantum algorithm whose complexity scales polynomially in the total number of input/output systems, in the dimension of the systems involved in each interaction, and in the inverse of the chosen threshold for the strength of the causal dependencies. Under additional assumptions, we also provide a second algorithm that has lower complexity and requires only local state preparation and local measurements. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography. Similarly, they can be used to identify useful communication channels in quantum networks, and to test the internal structure of uncharacterized quantum circuits.

复杂的过程通常来自一次涉及几个粒子的更简单的相互作用序列。然而，这些相互作用可能无法直接用于实验。在这里，我们开发了第一个有效的方法来解开多方量子过程中相互作用的因果结构，假设该过程具有有限的信息丢失并诱导其强度高于固定（但其他任意）阈值的因果依赖关系。我们的方法基于一种量子算法，其复杂性在输入/输出系统的总数、每个交互涉及的系统的维度以及因果依赖性强度的所选阈值的倒数中呈多项式缩放。在额外的假设下，我们还提供了第二种算法，它的复杂度较低，只需要本地状态准备和本地测量。我们的算法可用于识别可以通过量子过程断层扫描技术有效表征的过程。同样，它们可用于识别量子网络中有用的通信通道，并测试未表征的量子电路的内部结构。