  Federated learning is a framework that can learn from distributed networks.
It attempts to build a global model based on virtual fusion data without
sharing the actual data. Nevertheless, the traditional federated learning
process encounters two main challenges: high computational cost and message
transmission security. To address these challenges, we propose a quantum
federated learning for distributed quantum networks by utilizing interesting
characteristics of quantum mechanics. First, we give two methods to extract the
data information to the quantum state. It can cope with different acquisition
frequencies of data information. Next, a quantum gradient descent algorithm is
provided to help clients in the distributed quantum networks to train local
models. In other words, the algorithm gives the clients a mechanism to estimate
the gradient of the local model in parallel. Compared with the classical
counterpart, the proposed algorithm achieves exponential acceleration in
dataset scale and quadratic speedup in data dimensionality. And, a quantum
secure multi-party computation protocol is designed, which utilizes the Chinese
residual theorem. It could avoid errors and overflow problems that may occur in
the process of large number operation. Security analysis shows that this
quantum protocol can resist common external and internal attacks. Finally, to
demonstrate the effectiveness of the proposed framework, we use it to the train
federated linear regression model and execute essential computation steps on
the Qiskit quantum computing framework.
