# Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets

arXiv: https://arxiv.org/abs/2602.04943 · HTML: https://mlsanity.com/paper/2602.04943/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 8 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 1 of 1)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)

## Built on by (most cited first, 1 of 1)

- [Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo](https://mlsanity.com/paper/2605.13807/) (2026)

## Abstract (arXiv)

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 mathbbZ2 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.