We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems to $D>2$ dimensions. We obtain a local gap threshold of $\frac{3}{n}$, independent of $D$, for nearest-neighbor interactions. The $\frac{1}{n}$ scaling persists for arbitrary finite-range interactions in $\mathbb Z^3$. The key observation is that there is more flexibility in Knabe's combinatorial approach if one employs the operator Cauchy-Schwarz inequality.
Spectral gaps of ironed two-qubit gadgets matching the iSWAP gap
South China Agricultural University（华南农业大学）；Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（先进智能与计算研究所，科技研究局）；Division of Mathematical Sciences, Nanyang Technological University（南洋理工大学数学科学系）
Exact spectral gaps of random one-dimensional quantum circuits
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Department of Applied Physics, Gipuzkoa School of Engineering, University of the Basque Country (UPV/EHU)（巴斯克国立大学吉普斯夸工程学院应用物理系）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家理论部）；Quantum Science Center, Oak Ridge, TN 37931, USA（橡树岭量子科学中心）
Advanced Photonic and Electronic Sciences Division, US DEVCOM Army Research Laboratory（美国国防部陆军研究实验室先进光子与电子科学部）；Quantum Algorithms and Applications Collaboratory, Sandia National Laboratories（桑迪亚国家实验室量子算法与应用协作体）；Department of Physics, Loughborough University（拉夫堡大学物理系）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
