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Hybrid beamforming (HBF) is a key enabler for massive multiple-input multiple-output (MIMO) systems thanks to its capability to maintain significant spatial multiplexing gains with low hardware cost and power consumption. However, HBF optimizations are often challenging due to the nonconvexity and highly coupled analog and digital beamformers. In this paper, we propose an efficient HBF method based on deep unfolding to maximize the sum rate of large multiuser MIMO systems. We first derive closed-form expressions for the gradients of the sum rate with respect to the analog and digital beamformers to develop a projected gradient ascent (PGA) framework. We then incorporate this framework with the deep unfolding technique in an unfolded PGA deep neural network, which efficiently outputs reliable hybrid beamformers with low complexity and fast execution thanks to the well-trained hyperparameters. Numerical results show that the proposed method converges much faster than the conventional PGA scheme and significantly outperforms the conventional PGA and the successive convex approximation counterparts.