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Quality-Diversity (QD) optimization algorithms are a well-known approach to generate large collections of diverse and high-quality solutions. However, derived from evolutionary computation, QD algorithms are population-based methods which are known to be data-inefficient and requires large amounts of computational resources. This makes QD algorithms slow when used in applications where solution evaluations are computationally costly. A common approach to speed up QD algorithms is to evaluate solutions in parallel, for instance by using physical simulators in robotics. Yet, this approach is limited to several dozen of parallel evaluations as most physics simulators can only be parallelized more with a greater number of CPUs. With recent advances in simulators that run on accelerators, thousands of evaluations can now be performed in parallel on single GPU/TPU. In this paper, we present QDax, an accelerated implementation of MAP-Elites which leverages massive parallelism on accelerators to make QD algorithms more accessible. We show that QD algorithms are ideal candidates to take advantage of progress in hardware acceleration. We demonstrate that QD algorithms can scale with massive parallelism to be run at interactive timescales without any significant effect on the performance. Results across standard optimization functions and four neuroevolution benchmark environments shows that experiment runtimes are reduced by two factors of magnitudes, turning days of computation into minutes. More surprising, we observe that reducing the number of generations by two orders of magnitude, and thus having significantly shorter lineage does not impact the performance of QD algorithms. These results show that QD can now benefit from hardware acceleration, which contributed significantly to the bloom of deep learning.