Abstract Recently, there has been growing interest in the utilization of physical systems as heuristic optimizers for classical spin Hamiltonians. A prominent approach employs gain-dissipative optical oscillator networks for this purpose. Unfortunately, these systems inherently suffer from an inexact mapping between the oscillator network loss rate and the spin Hamiltonian due to additional degrees of freedom present in the system such as oscillation amplitude. In this work, we theoretically analyze and experimentally demonstrate a scheme for the alleviation of this difficulty. The scheme involves control over the laser oscillator amplitude through modification of individual laser oscillator loss. We demonstrate this approach in a laser network classical XY model simulator based on a digital degenerate cavity laser. We prove that for each XY model energy minimum there corresponds a unique set of laser loss values that leads to a network state with identical oscillation amplitudes and to phase values that coincide with the XY model minimum. We experimentally demonstrate an eight fold improvement in the deviation from the minimal XY energy by employing our proposed solution scheme.

中文翻译：

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通过激光损耗控制在激光网络损耗率和经典 XY 哈密顿量之间精确映射

摘要 最近，人们对利用物理系统作为经典自旋哈密顿量的启发式优化器越来越感兴趣。为此目的，一种突出的方法采用增益耗散光学振荡器网络。不幸的是，由于系统中存在额外的自由度，例如振荡幅度，这些系统固有地遭受振荡器网络损耗率和自旋哈密顿量之间的不精确映射。在这项工作中，我们从理论上分析并通过实验证明了缓解这一困难的方案。该方案涉及通过修改单个激光振荡器损耗来控制激光振荡器幅度。我们在基于数字简并腔激光器的激光网络经典 XY 模型模拟器中演示了这种方法。我们证明，对于每个 XY 模型能量最小值，对应一组独特的激光损耗值，导致具有相同振荡幅度的网络状态和与 XY 模型最小值一致的相位值。通过采用我们提出的解决方案，我们通过实验证明了与最小 XY 能量的偏差提高了八倍。