Capsule networks, which incorporate the paradigms of connectionism and
symbolism, have brought fresh insights into artificial intelligence. The
capsule, as the building block of capsule networks, is a group of neurons
represented by a vector to encode different features of an entity. The
information is extracted hierarchically through capsule layers via routing
algorithms. Here, we introduce a quantum capsule network (dubbed QCapsNet)
together with an efficient quantum dynamic routing algorithm. To benchmark the
performance of the QCapsNet, we carry out extensive numerical simulations on
the classification of handwritten digits and symmetry-protected topological
phases, and show that the QCapsNet can achieve an enhanced accuracy and
outperform conventional quantum classifiers evidently. We further unpack the
output capsule state and find that a particular subspace may correspond to a
human-understandable feature of the input data, which indicates the potential
explainability of such networks. Our work reveals an intriguing prospect of
quantum capsule networks in quantum machine learning, which may provide a
valuable guide towards explainable quantum artificial intelligence.

介绍了一种名为 QCapsNet 的量子胶囊网络，该网络通过一种高效的量子动态路由算法从胶囊层层抽取信息， 实现了对手写数字和对称保护拓扑相的分类任务。进一步分析发现，输出胶囊状态的一个子空间可能对应于输入数据的一个人类可理解的特征，暗示了这种网络的可解释性和价值。