A Sc₂C₂@C₈₈-cluster-based ultra-compact multilevel probabilistic bit for matrix multiplication

Information units are progressively approaching the fundamental physical limits of integration density, including in terms of extremely small sizes, multistates and probabilistic traversal. However, simultaneously encompassing all of these characteristics in a unit remains elusive. Here, via real-time in situ electrical monitoring, we clearly observed stochastic alterations of multiple conductance states in Sc₂C₂@C₈₈. The true random bit sequence generated exhibited an autocorrelation function whose confidence interval fell within ±0.02, demonstrating high-quality randomness. The alterations of multiple conductance states are controllable, that is, whose probability distributions could traverse from 0 to 1, enabling us to factorize 551 into its prime factors. Furthermore, we proposed a matrix-chain multiplication scheme and experimentally verified the multiplication of two 4 × 4 state-transition matrices with a small maximum error of <0.05. Combined with theoretical calculations, the stochastic but controllable multistates are probably attributed to the rich energy landscape, which could be stepwise changed by the electric field. Our findings reveal extremely small multilevel probabilistic bit for matrix multiplication, which pave the way for ultra-compact intelligent electronic devices.