标题： 均衡化超自旋机 显示英文标题

标题： Equalized Hyperspin Machine

摘要： 可靠地模拟自旋模型对于解决传统计算设备难以处理的复杂优化问题至关重要。 最近引入的超自旋机器，这是一个由线性和非线性耦合的参数振荡器组成的网络，提供了一个通用的经典矢量自旋模型的多功能模拟器，在任意维度中找到模拟自旋哈密顿量的最小值，并实现新颖的退火算法。 在超自旋机器中，振荡器随时间演化以最小化一个成本函数，为了使系统能够可靠地模拟目标自旋模型，该成本函数必须类似于所需的自旋哈密顿量。 如果超自旋振幅在稳态时相等，则满足这一条件。 目前，尚不存在一种机制来强制振幅相等。 在此，我们弥补了这一差距，并介绍了一种方法，在稳态中使振幅相等的情况下模拟超自旋机器。 我们采用了一个额外的振荡器网络（称为均衡器），通过反对称非线性耦合连接到超自旋机器，并均衡超自旋振幅。 我们通过大规模数值模拟，最多达到$10000$个超自旋，展示了这种均衡后的超自旋机器的性能。 与没有均衡的超自旋机器相比，我们发现均衡后的超自旋机器（i）能达到数量级更低的自旋能量，且（ii）其性能对系统参数的敏感性显著降低。 均衡后的超自旋机器提供了一个具有竞争力的自旋哈密顿量最小化器，并为将振幅均衡与复杂的退火协议相结合以进一步提升自旋机器的性能打开了可能性。 显示英文摘要

摘要： The reliable simulation of spin models is of critical importance to tackle complex optimization problems that are intractable on conventional computing machines. The recently introduced hyperspin machine, which is a network of linearly and nonlinearly coupled parametric oscillators, provides a versatile simulator of general classical vector spin models in arbitrary dimension, finding the minimum of the simulated spin Hamiltonian and implementing novel annealing algorithms. In the hyperspin machine, oscillators evolve in time minimizing a cost function that must resemble the desired spin Hamiltonian in order for the system to reliably simulate the target spin model. This condition is met if the hyperspin amplitudes are equal in the steady state. Currently, no mechanism to enforce equal amplitudes exists. Here, we bridge this gap and introduce a method to simulate the hyperspin machine with equalized amplitudes in the steady state. We employ an additional network of oscillators (named equalizers) that connect to the hyperspin machine via an antisymmetric nonlinear coupling and equalize the hyperspin amplitudes. We demonstrate the performance of such an equalized hyperspin machine by large-scale numerical simulations up to $10000$ hyperspins. Compared to the hyperspin machine without equalization, we find that the equalized hyperspin machine (i) Reaches orders of magnitude lower spin energy, and (ii) Its performance is significantly less sensitive to the system parameters. The equalized hyperspin machine offers a competitive spin Hamiltonian minimizer and opens the possibility to combine amplitude equalization with complex annealing protocols to further boost the performance of spin machines.