Spin Vector Control for Heisenberg-Inspired Probabilistic Computing

Abstract

Probabilistic bits (p-bits) have emerged as a cornerstone of probabilistic computing, enabling energy-efficient hardware implementation for probabilistic inference and combinatorial optimization. A critical challenge in advancing this field beyond binary p-bits lies in realizing and manipulating vector spin information, essential for mapping complex energy-based models such as the Heisenberg Hamiltonian.Here, we demonstrate a spintronic platform capable of real-space vector summation by using dual ferromagnetic spin injections into a monolayer graphene channel. By electrically tuning the spin polarization through independently controlled injection currents, we achieve continuous control over the magnitude and direction of the resulting spin accumulation vector. Experimental observations, supported by theoretical vector summation models and spin-circuit simulations, reveal coherent vector interactions and angular tunability of the spin state. This approach enables direct implementation of vector-based spin logic and lays the groundwork for mapping classical Heisenberg models using stochastic low-barrier magnets. Our results establish a scalable pathway for realizing probabilistic spin circuits based on two-dimensional materials, offering new opportunities for low-power, non-Boolean computing architectures.