A Deep Dive into the Computational Fidelity of High Variability Low Energy Barrier Magnet Technology for Accelerating Optimization and Bayesian Problems

TL;DR

This work assesses the computational fidelity of low energy barrier magnet–based p-bits for accelerating energy minimization and probabilistic graphical computing. Using a compact MATLAB model, it quantifies how device-level distortions—categorized as shifting and scaling of p-bit characteristics and energy-barrier variability—affect two algorithm families (EMOA, PGA), and compares sampling versus simulated annealing for reliability. Key findings show EMOA networks exhibit sub-linear MAE growth and benefit from larger sizes, while PGA networks experience linear-to-super-linear MAE growth, with large Bayesian networks particularly affected by barrier variability. The results provide certifiable error margins and design guidance for deploying LBMs as practical hardware accelerators for probabilistic and combinatorial optimization tasks.

Abstract

Low energy barrier magnet (LBM) technology has recently been proposed as a candidate for accelerating algorithms based on energy minimization and probabilistic graphs because their physical characteristics have a one-to-one mapping onto the primitives of these algorithms. Many of these algorithms have a much higher tolerance for error compared to high-accuracy numerical computation. LBM, however, is a nascent technology, and devices show high sample-to-sample variability. In this work, we take a deep dive into the overall fidelity afforded by this technology in providing computational primitives for these algorithms. We show that while the compute results show finite deviations from zero variability devices, the margin of error is almost always certifiable to a certain percentage. This suggests that LBM technology could be a viable candidate as an accelerator for popular emerging paradigms of computing.

Figures (8)

• Figure 1: (a) Illustrative schematic of an embedded RBM, an energy-based optimization and learning algorithm, in a dual-stacked feedback cross-bar structure with neurons (the compute units) at the edges (large circles), while the synaptic weights (the program) loaded in memristors located at the cross-points of the core cross-bar structure (small circles). The active neurons and synapses are colored bold (red and yellow), while inactive units are greyed out. (b) The RBM network that gets embedded in (a). The bidirectional blue lines represent the synaptic connections between the neurons (red circles). The yellow circles used in (a) are not shown here for simplicity. (c) The design of an LBM-magnetic tunnel junction (MTJ)-based p-bit unit. (d) Ideal characteristics of a p-bit device. (e) Schematics of different characteristics distortions. (f) Illustration of energy barrier variation in a nanomagnet. Symbols (diamond, square, etc.) in (e) and (f) represent different variabilities henceforth.
• Figure 2: Normalized MAE from horizontal shifting for (a) EMOA and (b) PGA with different network sizes (size of the $J$ matrix). In all subsequent figures, we measured the average and standard deviation of the MAE from $100$ simulations. Colored lines in each figure represent different network sizes, and different symbols represent different distortions introduced in Fig. \ref{['fig1']}(e). Inset in (a) shows the schematic of a $3 \times 3$ EMOA network, while inset in (b) shows the schematic of an $8 \times 8$ PGA Bayesian network representing a family tree (GF: Grandfather, etc.).
• Figure 3: Normalized MAE from vertical shifting for (a) EMOA and (b) PGA with different network sizes.
• Figure 4: Normalized MAE from horizontal scaling for (a) EMOA and (b) PGA with different network sizes.
• Figure 5: Normalized MAE from vertical scaling for (a) EMOA and (b) PGA with different network sizes.