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We present Q-functionals, an alternative architecture for continuous control deep reinforcement learning. Instead of returning a single value for a state-action pair, our network transforms a state into a function that can be rapidly evaluated in parallel for many actions, allowing us to efficiently choose high-value actions through sampling. This contrasts with the typical architecture of off-policy continuous control, where a policy network is trained for the sole purpose of selecting actions from the Q-function. We represent our action-dependent Q-function as a weighted sum of basis functions (Fourier, Polynomial, etc) over the action space, where the weights are state-dependent and output by the Q-functional network. Fast sampling makes practical a variety of techniques that require Monte-Carlo integration over Q-functions, and enables action-selection strategies besides simple value-maximization. We characterize our framework, describe various implementations of Q-functionals, and demonstrate strong performance on a suite of continuous control tasks.