The Complexity of Local Stoquastic Hamiltonians on 2D Lattices
Gabriel Waite and Michael J. Bremner
Quantum 10, 2097 (2026). https://doi.org/10.22331/q-2026-05-06-2097 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 con