Tuning the probability distribution of a quantum bistable optical system

Probabilistic computing based on electronic implementations has shown promising applications in integer factorization and other types of combinatorial problems. Its key building block, a probabilistic bit (p-bit), consists of a tunable random number generator whose probability distribution can be tailored on-demand. We demonstrate an optical p-bit based on the spontaneous symmetry breaking of a bi-stable system. Optical parametric oscillators (OPO) are bistable nonlinear systems in which the phase of a down-converted signal ω can take two discrete values (0 or π). The randomness of the measured phase originates from the quantum vacuum field and is therefore truly random. We show coherent control of the OPO's phase probability distribution, exhibiting a continuous transition from purely random (50/50 distribution of 0/π phase) to purely deterministic (phase determined by the bias field). We first confirm that the two possible phases occur with equal probability, verifying the randomness dictated by the vacuum field fluctuations. We then introduce a controlled bias field at the signal frequency ω into the optical cavity to skew the probability distribution, showing continuous tuning of the signal's output phase distribution, as a function of the phase offset between the bias and pump fields. Optical probabilistic computing schemes should enable orders-of-magnitude speed enhancements on challenging tasks such as inference in Bayesian neural networks and combinatorial optimization.