Quantum federated learning (QFL) enables clients to train quantum neural network (QNN) models without exposing private data. Conventional aggregation becomes unstable when data are heterogeneous, communication is unreliable, fidelity varies, latency is present, or quantum hardware introduces noise. Moreover, many QNN parameters are periodic angles, so Euclidean averaging often fails to respect their circular nature. To address these issues we introduce a self‑consistent midpoint aggregation method for robust QFL. The method comprises three key components: (1) QoS‑aware client weighting that gives higher‑quality links larger influence; (2) circular parameter aggregation that averages angles modulo $2\pi$; (3) bounded midpoint‑based update control that limits abrupt jumps. Validation on synthetic angular tests and real IBM quantum machines confirms that the approach markedly improves stability and reduces volatility. Extensive experiments on medical and financial datasets further demonstrate that the method achieves competitive accuracy while delivering lower variance and smoother convergence.
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