  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.
