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Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets
Mahmud Ashraf Shamim, Md Moshiur Rahman Raj, Mohamed Hibat-Allah, Paulo T Araujo·February 4, 2026
cond-mat.str-elcond-mat.dis-nnAIComplexityQuantum Physics
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Abstract
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.