A functionally reversible probabilistic computing architecture enabled by interactions of current-controlled magnetic devices

TL;DR

This work presents a new physical implementation of ferromagnetic disks whose magnetization switching process is triggered by current pulses, skewed by external magnetic fields, and randomized by ambient thermal noise, and achieves a highly accurate bidirectional one-bit full-adder, a proof of concept for complex multi-gate logic functions with reversible information flow.

Abstract

Probabilistic computers replace logic gates with networks of interacting random variables, creating bidirectional systems that can back-derive inputs from outputs. Such architectures enable efficient generation of random samples, implementations of novel algorithms, and natural solutions to classically hard problems such as prime factorization. We present a new physical implementation for these networks: ferromagnetic disks whose magnetization switching process is triggered by current pulses, skewed by external magnetic fields, and randomized by ambient thermal noise. We show that geometry-dependent magnetostatic interactions between these magnetic cells lead to system behavior that emulates deterministic logic gates. Furthermore, by chaining multiple "gates," we achieve a highly accurate bidirectional one-bit full-adder, a proof of concept for complex multi-gate logic functions with reversible information flow. This analog magnetic probabilistic computer methodology improves on other implementations in speed, tunability, and energy efficiency, thereby enabling a powerful new pathway towards practical solution of classically hard problems.

Figures (4)

• Figure 1: Probabilistic switching dynamics in an SOT-MRAM cell. (A) In our devices, a magnetization $\hat{m}$ starting from the red regions will damp to the left-pointing "0" state; an $\hat{m}$ starting from the blue regions will precess to the right-pointing "1" state. A spin pulse with magnitude $\eta$ and angle $\beta$ will send $\hat{m}$ along a preset trajectory. The path shown in white corresponds to large $\eta$ and $\beta = 90^{\circ}$; it sends $\hat{m}$ to the exact borderline between the two regions. (B) Time-resolved magnetization trajectories in this scenario: the final state of the SOT-MRAM cell is a random variable determined by ambient thermal fluctuations.
• Figure 2: Switching and interaction parameters. (A) The probability of the magnetization falling to the "1" state is a sigmoid with respect to the external field in the $x$-direction. The scaling factor depends on the temperature and anisotropy constant of the device. (B) The interaction parameter $J_{ij}$ between magnets (i.e., the input to the sigmoid) depends on the cell-to-cell distance vector, $(x_j - x_i)\hat{\mathbf{x}} + (y_j - y_i)\hat{\mathbf{y}}$, which is here represented with polar coordinates $b$ and $\psi$. Note positive $J_{ij}$ along the easy axis and negative $J_{ij}$$90^{\circ}$ away.
• Figure 3: Logic gate networks. (A) The three-bit geometric arrangement corresponding to a probabilistic AND gate. (B) Cycling the AND gate. The system naturally falls into the $ABC$ states that match the deterministic truth table: 000, 010, 100, and 111. Fixing the output $C$ through an additional bias backpropagates to the input states $AB$: setting $C = 1$ isolates the $AB = 11$ state, while setting $C = 0$ leads the system to the other three $AB$ possibilities. (C) All 10 probabilistic logic functions of two inputs and one output that can be produced with the reconfigurable gate, which is a five-bit geometric arrangement. The same gate can be reconfigured on demand into an AND, OR, NAND, etc.
• Figure 4: A one-bit full adder. (A) The circuit schematic, comprised of two connected half-adders and seven probabilistic gate regions. (B) The forward pass: we calculate the correct two-bit sum $C_{\text{out}}S_{\text{out}}$ with $\sim 90\%$ accuracy. (C) The backwards pass: with the same architecture, we can fix the outputs and back-derive the inputs $A$, $B$, and $C_{\text{in}}$. For instance, setting $C_{\text{out}}S_{\text{out}} = 11$ (that is, 3) leads us back to the correct input calculation: 1 + 1 + 1.