We study the computational complexity of learning the ground state phase structure of Heisenberg antiferromagnets. Representing Hilbert space as a weighted graph, the variational energy defines a weighted XY model that, for $\mathbb{Z}_2$ phases, reduces to a classical antiferromagnetic Ising model on that graph. For fixed amplitudes, reconstructing the signs of the ground state wavefunction thus reduces to a weighted Max-Cut instance. This establishes that ground state phase reconstruction for Heisenberg antiferromagnets is worst-case NP-hard and links the task to combinatorial optimization.

翻译：我们研究了学习海森堡反铁磁体基态相结构的计算复杂性。将希尔伯特空间表示为加权图后，变分能量定义了一个加权XY模型，对于$\mathbb{Z}_2$相位，该模型在该图上简化为经典的反铁磁伊辛模型。因此，在振幅固定的情况下，重构基态波函数的符号简化为一个加权Max-Cut实例。这确立了海森堡反铁磁体的基态相位重构在最坏情况下是NP难的，并将该任务与组合优化联系起来。