Automatic Extraction and Compensation of P-Bit Device Variations in Large Array Utilizing Boltzmann Machine Training

Abstract: Probabilistic Bit (P-Bit) device serves as the core hardware for implementing Ising computation. However, the severe intrinsic variations of stochastic P-Bit devices hinder the large-scale expansion of the P-Bit array, significantly limiting the practical usage of Ising computation. In this work, a behavioral model which attributes P-Bit variations to two parameters {\alpha} and {\Delta}V is proposed. Then the weight compensation method is introduced, which can mitigate {\alpha} and {\Delta}V of P-Bits device variations by rederiving the weight matrix, enabling them to compute as ideal identical PBits without the need for weights retraining. Accurately extracting the {\alpha} and {\Delta}V simultaneously from a large P-Bit array which is prerequisite for the weight compensation method is a crucial and challenging task. To solve this obstacle, we present the novel automatic variation extraction algorithm which can extract device variations of each P-Bit in a large array based on Boltzmann machine learning. In order for the accurate extraction of variations from an extendable P-Bit array, an Ising Hamiltonian based on 3D ferromagnetic model is constructed, achieving precise and scalable array variation extraction. The proposed Automatic Extraction and Compensation algorithm is utilized to solve both 16-city traveling salesman problem(TSP) and 21-bit integer factorization on a large P-Bit array with variation, demonstrating its accuracy, transferability, and scalability.