标题： 用于磁隧道结玻尔兹曼机的Toffoli门 gadget 显示英文标题

标题： A Toffoli Gadget for Magnetic Tunnel Junctions Boltzmann Machines

摘要： 磁性隧道结（MTJs）对于非常规计算应用具有极大的兴趣。 Toffoli门是一种通用可逆逻辑门，能够构建任意布尔电路。 在这里，我们展示了一种概念验证的构建装置，该装置将Toffoli门的真值表编码到耦合单轴纳米磁体的基态中，这些纳米磁体可以形成垂直磁化MTJ的自由层。 该构建具有三个输入位、三个输出位和一个辅助位。 我们数值模拟了七个巨自旋在随机朗道-利夫希茨-吉布斯（s-LLG）方程下的演化。 我们研究了各向异性与交换耦合强度比值$H_A/H_\text{ex}$对设备工作的影响。 我们发现，对于$H_A/H_\text{ex} \lesssim 0.93$，自旋仅在LLG动力学下演化为Toffoli门真值表配置，而更高的$H_A/H_\text{ex}$比值由于次优亚稳态需要热退火。 在我们选择的退火程序下，具有热退火的s-LLG模拟在$H_A/H_\text{ex}\simeq3.0$范围内实现了100%的成功率。 基于MTJ自由层构建Toffoli门的可行性凸显了它们在设计新型MTJ电路中的潜力。 显示英文摘要

摘要： 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.