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.

翻译：我们证明了二维正方量子比特格点上的2-局域随机哈密顿量问题是StoqMA完备的。我们通过扩展Oliveira和Terhal提出的空间稀疏电路构造方法，以及Bravyi、DiVincenzo、Oliveira和Terhal提出的微扰工具来实现这一结论。我们的主要贡献在于证明了StoqMA电路可以实现空间稀疏化，并且能够在无需增加粒子维度的情况下，构造出保持几何结构与随机性特征的微扰工具。