Random number generation driven by voltage-controlled magnetic anisotropy and their use in probabilistic computing

Ising machines are becoming increasingly popular as efficient and hardware-friendly solvers for combinatorial optimization problems. One promising approach for solving Ising models is through probabilistic Ising machines (PIMs), wherein conventional bits are replaced by bistable tunable stochastic bits (p-bits). The generation of random numbers is a crucial component of PIMs. Stochastic magnetic tunnel junctions (MTJs) have been proposed to physically implement p-bits; however, their scalability faces challenges due to the required fine tuning of a small energy barrier. Alternatively, the voltage-controlled magnetic anisotropy (VCMA) effect in deterministic perpendicular MTJs can be used to generate random binary states. Here, we present a comprehensive phase diagram to delineate the characteristics of VCMA pulses for the generation of true random numbers. We introduce the design of an MTJ-based p-bit, where the precision of the stochastic component is linked to the number of MTJs employed. We explore the impact of adaptive p-bit precision in solving an instance of a maximum satisfiability problem. The results show that a limited number of VCMA-based MTJs (less than 20) are sufficient to ensure performance comparable to the software solutions.