Cross-modal retrieval aims to search for data with similar semantic meanings across different content modalities. However, cross-modal retrieval requires huge amounts of storage and retrieval time since it needs to process data in multiple modalities. Existing works focused on learning single-source compact features such as binary hash codes that preserve similarities between different modalities. In this work, we propose a jointly learned deep hashing and quantization network (HQ) for cross-modal retrieval. We simultaneously learn binary hash codes and quantization codes to preserve semantic information in multiple modalities by an end-to-end deep learning architecture. At the retrieval step, binary hashing is used to retrieve a subset of items from the search space, then quantization is used to re-rank the retrieved items. We theoretically and empirically show that this two-stage retrieval approach provides faster retrieval results while preserving accuracy. Experimental results on the NUS-WIDE, MIR-Flickr, and Amazon datasets demonstrate that HQ achieves boosts of more than 7% in precision compared to supervised neural network-based compact coding models.