  Recent success in deep neural networks has generated strong interest in
hardware accelerators to improve speed and energy consumption. This paper
presents a new type of photonic accelerator based on coherent detection that is
scalable to large ($N \gtrsim 10^6$) networks and can be operated at high (GHz)
speeds and very low (sub-aJ) energies per multiply-and-accumulate (MAC), using
the massive spatial multiplexing enabled by standard free-space optical
components. In contrast to previous approaches, both weights and inputs are
optically encoded so that the network can be reprogrammed and trained on the
fly. Simulations of the network using models for digit- and
image-classification reveal a "standard quantum limit" for optical neural
networks, set by photodetector shot noise. This bound, which can be as low as
50 zJ/MAC, suggests performance below the thermodynamic (Landauer) limit for
digital irreversible computation is theoretically possible in this device. The
proposed accelerator can implement both fully-connected and convolutional
networks. We also present a scheme for back-propagation and training that can
be performed in the same hardware. This architecture will enable a new class of
ultra-low-energy processors for deep learning.
