Toffoli gadget for magnetic-tunnel-junction Boltzmann machines

Magnetic tunnel junctions (MTJs) are of great interest for nonconventional 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 that 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 Landau-Lifshitz-Gilbert (LLG) equation and stochastic LLG (sLLG) equation with a temperature annealing schedule. We investigate the effect of the anisotropy-to-exchange-coupling strength ratio H/H on the working of the gadget. We find that for HA/Hex≲0.93, the spins evolve to the Toffoli gate truth table configurations under LLG dynamics alone, while higher HA/Hex ratios require thermal annealing due to suboptimal metastable states. Under our chosen annealing procedure, the sLLG simulation with thermal annealing achieves a 100% success rate up to HA/Hex≃3.0. The results indicate a desirable choice of HA≃Hex for constructing the Toffoli gate. The feasibility of constructing MTJ-free-layer-based Toffoli gates highlights their potential in designing new types of MTJ-based circuits.