具有可编程自旋电路的海森堡机器
Heisenberg machines with programmable spin-circuits
AI总结：
本研究利用石墨烯长自旋扩散长度与低势垒磁体快速涨落特性，构建可编程自旋电路海森堡机器，可作为连续变量优化硬件求解器，并验证了概率计算可行性。
摘要：
我们证明，可以利用两项最新的实验进展，为统计物理中的经典海森堡模型构建紧凑的硬件仿真器。第一项进展是实验证实石墨烯中即使在室温下，自旋扩散长度也可超过微米量级；第二项是低势垒磁体（LBMs）的实验演示，其磁化强度甚至能以亚纳秒速率快速涨落。\n借助经实验验证的电路模型，我们表明，由外部电流源驱动的LBM阵列的稳态分布，对应于能量函数形式为$E = -1/2\sum_{i,j} J_{ij} (\hat{m}_i \cdot \hat{m}_j)$的经典系统。这一结论对于非平衡系统而言或许出人意料，但我们通过构造与耦合朗道-利夫希茨-吉尔伯特（LLG）方程系统对应的李雅普诺夫函数，证明了该结论的合理性。我们构造的李雅普诺夫函数描述了LBMs通过其注入自旋中性衬底的自旋电流发生相互作用的过程。\n我们提出了调节耦合系数$J_{ij}$的方法，使该系统可作为硬件求解器，用于求解由矢量磁化强度表示的连续变量优化问题，其作用类似于伊辛模型在求解二元变量优化问题中的角色。最后，我们基于四个耦合的随机LLG方程网络训练了一个海森堡异或门，验证了可编程海森堡模型实现概率计算的概念。
英文摘要：
We show that we can harness two recent experimental developments to build a compact hardware emulator for the classical Heisenberg model in statistical physics. The first is the demonstration of spin-diffusion lengths in excess of microns in graphene even at room temperature. The second is the demonstration of low barrier magnets (LBMs) whose magnetization can fluctuate rapidly even at sub-nanosecond rates. Using experimentally benchmarked circuit models, we show that an array of LBMs driven by an external current source has a steady-state distribution corresponding to a classical system with an energy function of the form $E = -1/2\sum_{i,j} J_{ij} (\hat{m}_i \cdot \hat{m}_j$). This may seem surprising for a non-equilibrium system but we show that it can be justified by a Lyapunov function corresponding to a system of coupled Landau-Lifshitz-Gilbert (LLG) equations. The Lyapunov function we construct describes LBMs interacting through the spin currents they inject into the spin neutral substrate. We suggest ways to tune the coupling coefficients $J_{ij}$ so that it can be used as a hardware solver for optimization problems involving continuous variables represented by vector magnetizations, similar to the role of the Ising model in solving optimization problems with binary variables. Finally, we train a Heisenberg XOR gate based on a network of four coupled stochastic LLG equations, illustrating the concept of probabilistic computing with a programmable Heisenberg model.
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