  Quantum federated learning (QFL) can facilitate collaborative learning across
multiple clients using quantum machine learning (QML) models, while preserving
data privacy. Although recent advances in QFL span different tasks like
classification while leveraging several data types, no prior work has focused
on developing a QFL framework that utilizes temporal data to approximate
functions useful to analyze the performance of distributed quantum sensing
networks. In this paper, a novel QFL framework that is the first to integrate
quantum long short-term memory (QLSTM) models with temporal data is proposed.
The proposed federated QLSTM (FedQLSTM) framework is exploited for performing
the task of function approximation. In this regard, three key use cases are
presented: Bessel function approximation, sinusoidal delayed quantum feedback
control function approximation, and Struve function approximation. Simulation
results confirm that, for all considered use cases, the proposed FedQLSTM
framework achieves a faster convergence rate under one local training epoch,
minimizing the overall computations, and saving 25-33% of the number of
communication rounds needed until convergence compared to an FL framework with
classical LSTM models.
