Title: Sample efficient Quality Diversity for neural continuous control. Abstract: We propose a novel Deep Neuroevolution algorithm, QD-RL, that combines the strengths of off-policy reinforcement learning (RL) algorithms and Quality Diversity (QD) approaches to solve continuous control problems with neural controllers. The QD part contributes structural biases by decoupling the search for diversity from the search for high return, resulting in efficient management of the exploration-exploitation trade-off. The RL part contributes sample efficiency by relying on off-policy gradient-based updates of the agents. More precisely, we train a population of off-policy deep RL agents to simultaneously maximize diversity within the population and the return of each individual agent. QD-RL selects agents interchangeably from a Pareto front or from a Map-Elites grid, resulting in stable and efficient population updates. Our experiments in the Ant-Maze and Ant-Trap environments show that QD-RL can solve challenging exploration and control problems with deceptive rewards while being two orders of magnitude more sample efficient than the evolutionary counterpart.