Deep neural networks (DNNs) have become very popular in many areas, especially classification and prediction. However, as the number of neurons in the DNN increases to solve more complex problems, the DNN becomes limited by the latency and power consumption of existing hardware. A scalable, ultra-low latency photonic tensor processor can compute DNN layer outputs in a single shot. The processor includes free-space optics that perform passive optical copying and distribution of an input vector and integrated optoelectronics that implement passive weighting and the nonlinearity. An example of this processor classified the MNIST handwritten digit dataset (with an accuracy of 94%, which is close to the 96% ground truth accuracy). The processor can be scaled to perform near-exascale computing before hitting its fundamental throughput limit, which is set by the maximum optical bandwidth before significant loss of classification accuracy (determined experimentally).