Modeling a Toffoli Gate Constructed Using Perpendicular Magnetic Tunnel Junctions

Abstract

Magnetic Tunnel Junctions (MTJs) are of great interest for non-conventional computing applications. One prominent application is reversible computing, due to its energy-efficient and information-preserving nature. The Toffoli gate plays a crucial role as a universal reversible logic gate, enabling the construction of reversible circuits. Here we present a proof-of-concept construction of a classical Toffoli gate using seven coupled uniaxial nanomagnets that could form the free layer of perpendicularly magnetized MTJs. This construction maps seven spins to three input bits, three output bits, and one ancilla bit, encoding the Toffoli gate's truth table as the system's ground state. We use Python to numerically simulate the system, with the seven coupled macrospins evolving under the stochastic Landau–Lifshitz–Gilbert (sLLG) equation and a two-stage Runge-Kutta integration scheme. Our results demonstrate that the system evolves to the Toffoli gate truth table with a thermal annealing process. Additionally, we also consider the zero temperature case, where the system’s evolution is governed solely by the LLG equation. We observe that the anisotropy energy shapes the system’s energy landscape. With very low anisotropy energy ($E_A$∼1$k_B$T), spins evolve to the ground state configurations, while higher anisotropy energy causes the spins to become trapped in metastable states. Our exploration of the rich LLG dynamical behaviors suggests significant potential for future computational applications. *This project is supported by the Office of Naval Research (ONR) under award number N00014-23-1-2771.