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Abstract 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 proposedfederated 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.