  Probabilistic computing has emerged as a viable approach to solve hard
optimization problems. Devices with inherent stochasticity can greatly simplify
their implementation in electronic hardware. Here, we demonstrate intrinsic
stochastic resistance switching controlled via electric fields in perovskite
nickelates doped with hydrogen. The ability of hydrogen ions to reside in
various metastable configurations in the lattice leads to a distribution of
transport gaps. With experimentally characterized p-bits, a shared-synapse
p-bit architecture demonstrates highly-parallelized and energy-efficient
solutions to optimization problems such as integer factorization and
Boolean-satisfiability. The results introduce perovskite nickelates as scalable
potential candidates for probabilistic computing and showcase the potential of
light-element dopants in next-generation correlated semiconductors.
