  Probabilistic machine learning utilizes controllable sources of randomness to
encode uncertainty and enable statistical modeling. Harnessing the pure
randomness of quantum vacuum noise, which stems from fluctuating
electromagnetic fields, has shown promise for high speed and energy-efficient
stochastic photonic elements. Nevertheless, photonic computing hardware which
can control these stochastic elements to program probabilistic machine learning
algorithms has been limited. Here, we implement a photonic probabilistic
computer consisting of a controllable stochastic photonic element - a photonic
probabilistic neuron (PPN). Our PPN is implemented in a bistable optical
parametric oscillator (OPO) with vacuum-level injected bias fields. We then
program a measurement-and-feedback loop for time-multiplexed PPNs with
electronic processors (FPGA or GPU) to solve certain probabilistic machine
learning tasks. We showcase probabilistic inference and image generation of
MNIST-handwritten digits, which are representative examples of discriminative
and generative models. In both implementations, quantum vacuum noise is used as
a random seed to encode classification uncertainty or probabilistic generation
of samples. In addition, we propose a path towards an all-optical probabilistic
computing platform, with an estimated sampling rate of ~ 1 Gbps and energy
consumption of ~ 5 fJ/MAC. Our work paves the way for scalable, ultrafast, and
energy-efficient probabilistic machine learning hardware.
