The Complexity of Local Stoquastic Hamiltonians on 2D Lattices
Quantum Physics
2026-05-06 v4 Computational Complexity
Abstract
We show the 2-Local Stoquastic Hamiltonian problem on a 2D square qubit lattice is StoqMA-complete. We achieve this by extending the spatially sparse circuit construction of Oliveira and Terhal, as well as the perturbative gadgets of Bravyi, DiVincenzo, Oliveira, and Terhal. Our main contributions demonstrate StoqMA circuits can be made spatially sparse and that geometrical, stoquastic-preserving, perturbative gadgets can be constructed, without an increase to particle dimension.
Keywords
Cite
@article{arxiv.2502.14244,
title = {The Complexity of Local Stoquastic Hamiltonians on 2D Lattices},
author = {Gabriel Waite and Michael J. Bremner},
journal= {arXiv preprint arXiv:2502.14244},
year = {2026}
}
Comments
35 + 8 pages, 15 + 3 figures. v4 - accepted Quantum version