I agree with dbfclark that it's case by case. At Skymind (https://skymind.io/), we support an open-source Java library (http://deeplearning4j.org/).
* So obviously Java, Scala, Clojure, and lower-level languages like C++, C and CUDA.
* Since deep learning needs very large datasets to train on, our engineers need experience with open-source libraries used in production environments, such as Hadoop, Spark, Kafka. We also work with Lagom, Nifi, etc.
* A lot of the same math underpins many machine learning and deep learning algorithms. So a high degree of comfort with linear algebra, calculus and probability is a plus.
* A general knowledge of the strengths and weaknesses of various algorithms -- neural networks, reinforcement learning, etc. -- their combinations and applications is helpful.
The Github repos are here if you're curious: