We demonstrate how to compute the low energy spectrum for small ($N\le 50$), but otherwise arbitrary, spin-glass instances using modern Graphics Processing Units or similar heterogeneous architecture. Our algorithm performs an exhaustive (i.e., brute-force) search of all possible configurations to select $S\ll 2^N$ lowest ones together with their corresponding energies. We mainly focus on the Ising model defined on an arbitrary graph. An open-source implementation based on CUDA Fortran and a suitable Python wrapper are provided. As opposed to heuristic approaches, ours is exact and thus can serve as a references point to benchmark other algorithms and hardware, including quantum and digital annealers. Our implementation offers unprecedented speed and efficiency already visible on commodity hardware. At the same time, it can be easily launched on professional, high-end graphics cards virtually at no extra effort. As a practical application, we employ it to demonstrate that the recent Matrix Product State based algorithm-despite its one-dimensional nature-can still accurately approximate the low energy spectrum of fully connected graphs of size $N$ approaching $50$.

中文翻译：

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CUDA 的强制自旋玻璃问题

我们演示了如何使用现代图形处理单元或类似的异构架构计算小（$N\le 50$）但其他任意的自旋玻璃实例的低能谱。我们的算法对所有可能的配置进行详尽的（即，蛮力）搜索，以选择 $S\ll 2^N$ 最低配置及其相应的能量。我们主要关注在任意图上定义的 Ising 模型。提供了基于 CUDA Fortran 的开源实现和合适的 Python 包装器。与启发式方法相反，我们的方法是精确的，因此可以作为对其他算法和硬件（包括量子和数字退火器）进行基准测试的参考点。我们的实施提供了前所未有的速度和效率，这在商用硬件上已经可见。同时，它可以轻松地在专业的高端显卡上启动，几乎无需额外的努力。作为一个实际应用，我们用它来证明最近的基于矩阵乘积状态的算法 - 尽管它是一维的 - 仍然可以准确地逼近大小为 $N$ 接近 $50$ 的全连接图的低能谱。