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Mixture of Experts (MoE) models with conditional execution of sparsely activated layers have enabled training models with a much larger number of parameters. As a result, these models have achieved significantly better quality on various natural language processing tasks including machine translation. However, it remains challenging to deploy such models in real-life scenarios due to the large memory requirements and inefficient inference. In this work, we introduce a highly efficient inference framework with several optimization approaches to accelerate the computation of sparse models and cut down the memory consumption significantly. While we achieve up to 26x speed-up in terms of throughput, we also reduce the model size almost to one eighth of the original 32-bit float model by quantizing expert weights into 4-bit integers. As a result, we are able to deploy 136x larger models with 27% less cost and significantly better quality compared to the existing solutions. This enables a paradigm shift in deploying large scale multilingual MoE transformers models replacing the traditional practice of distilling teacher models into dozens of smaller models per language or task.