A Toffoli Gadget for Magnetic Tunnel Junctions Boltzmann Machines

TL;DR

This paper proposes a magnetic nanomagnet-based gadget that encodes the Toffoli gate's truth table, demonstrating potential for MTJ-based reversible logic circuits through numerical simulations and thermal annealing techniques.

Contribution

It introduces a novel nanomagnet configuration for implementing the Toffoli gate within magnetic tunnel junctions, supported by simulation results showing high success rates.

Findings

Successful encoding of Toffoli gate in nanomagnet ground states

High success rate (up to 100%) with thermal annealing for certain anisotropy ratios

Feasibility of MTJ-free-layer-based Toffoli gates for circuit design

Abstract

Magnetic Tunnel Junctions (MTJs) are of great interest for non-conventional computing applications. The Toffoli gate is a universal reversible logic gate, enabling the construction of arbitrary boolean circuits. Here, we present a proof-of-concept construction of a gadget which encodes the Toffoli gate's truth table into the ground state of coupled uniaxial nanomagnets that could form the free layers of perpendicularly magnetized MTJs. This construction has three input bits, three output bits, and one ancilla bit. We numerically simulate the seven macrospins evolving under the stochastic Landau-Lifshitz-Gilbert (s-LLG) equation. We investigate the effect of the anisotropy-to-exchange-coupling strength ratio $H_A/H_\text{ex}$ on the working of the gadget. We find that for $H_A/H_\text{ex} \lesssim 0.93$, the spins evolve to the Toffoli gate truth table configurations under LLG dynamics alone, while higher $H_A/H_\text{ex}$ ratios require thermal annealing due to suboptimal metastable states. Under our chosen annealing procedure, the s-LLG simulation with thermal annealing achieves a 100% success rate up to $H_A/H_\text{ex}\simeq3.0$. The feasibility of constructing MTJ-free-layer-based Toffoli gates highlights their potential in designing new types of MTJ-based circuits.