Analog physical neural networks offer promising advancements in energy efficiency and computational speed over their digital counterparts but are typically operated in rather high-power regimes to maintain a sufficient signal-to-noise ratio (SNR). What happens if an analog system is instead operated in an ultra-low-power regime, in which the behavior of the system becomes highly stochastic and the noise is no longer a small perturbation on the signal? We immerse ourselves in the intricate dance of optical neural networks at quantum limits, where neuron activations hinge on the solitary act of a photon’s arrival, orchestrated by quantum uncertainty. Despite the overwhelming noise levels (SNR ≈ 1), our research successfully demonstrates that stochastic neural networks can be precisely trained to perform deterministic tasks with high accuracy. The methodology developed for training incorporates the stochastic nature of photon detection as a fundamental aspect. We experimentally demonstrated show a 98% accuracy for MNIST classification using an optical neural network with a hidden layer functioning at the single-photon level, utilizing only 0.008 photons per multiply-accumulate (MAC) operation, or 0.003 attojoules per MAC. Our experiment showed a greater than 40-fold reduction in photon use per inference compared to previous efforts without compromising accuracy. These findings underscore the viability of harnessing highly stochastic analog systems, even those dominated by inevitable quantum noise, for reliable neural network operations when trained appropriately.

Shi-Yuan Ma is a senior PhD candidate at Cornell University, working with Prof. Peter McMahon from 2019. His doctoral research is centered on optical computing and quantum optics, and he is eager to extend his exploration to diverse computational platforms. Shi-Yuan’s research interests focus on harnessing the potential computational power of physical systems, particularly through the use of machine learning techniques to train and analyze complex (stochastic) data and mechanisms. Prior to Cornell University, Shi-Yuan received his B.S. degree in Physics from University of Science and Technology of China, with a minor in Computer Science.