发表机构
The Rachel and Selim Benin School of Engineering and Computer Science; The Hebrew University of Jerusalem（Rachel和Selim Benin工程与计算机科学学院; 耶路撒冷希伯来大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究单交互哈密顿量模型，通过精确编译器将任意局域交互归约为单一交互，证明其QMA/StoqMA完备性，表明独立选择局域矩阵并非复杂性现象所必需。
AI 中文摘要
我们研究了在每一个局域项都是同一固定交互的无权重出现这一限制下，局域哈密顿量问题的复杂性。在由此产生的单交互哈密顿量（SIH）模型中，一旦交互被固定，哈密顿量就完全由其有序交互超图指定。我们的主要技术工具是一个精确编译器，它将任何固定的局域交互的有限字母表转换为单个交互。在一个指定的辅助子空间上，编译后的哈密顿量精确地重现了源哈密顿量，而在选定的分离尺度以下的完整谱则以多重性被保留。结合有限字母表归一化，这给出了从$k$-局域哈密顿量到SIH$_{3k+3}$的通用多项式时间归约，直至一个已知的全局能量尺度和逆多项式近似。更精细的构造给出了SIH$_3$以及具有有界度和交互范围的几何局域SIH$_8$的QMA完备性。在stoquastic设定中，我们获得了Stoq-SIH$_3$的StoqMA完备性和1-Pinned Stoq-SIH$_4$的QMA完备性。我们还建立了对于均匀系统大小依赖交互的困难性结果，并推导了哈密顿量量子PCP猜想、无挫折、指数精确和引导局域哈密顿量问题的单交互表述。这些结果表明，独立选择的局域矩阵和独立可调的耦合强度对于广泛的哈密顿量复杂性现象并非必要。
英文摘要
We study the complexity of Local Hamiltonian problems under the restriction that every local term is an unweighted occurrence of the same fixed interaction. In the resulting Single-Interaction Hamiltonian (SIH) model, once the interaction is fixed, the Hamiltonian is specified entirely by its ordered interaction hypergraph. Our main technical tool is an exact compiler that converts any fixed finite alphabet of local interactions into a single interaction. On a designated auxiliary subspace, the compiled Hamiltonian reproduces the source Hamiltonian exactly, while the complete spectrum below a chosen separation scale is preserved with multiplicity. Combined with a finite-alphabet normalization, this gives a universal polynomial-time reduction from $k$-Local Hamiltonian to SIH$_{3k+3}$ up to a known global energy scale and inverse-polynomial approximation. Sharper constructions give QMA-completeness of SIH$_3$ and of geometrically local SIH$_8$ with bounded degree and interaction range. In the stoquastic setting, we obtain StoqMA-completeness of Stoq-SIH$_3$ and QMA-completeness of 1-Pinned Stoq-SIH$_4$. We also establish hardness results for uniformly system-size-dependent interactions and derive single-interaction formulations of the Hamiltonian quantum PCP conjecture, frustration-free, exponentially precise, and guided Local Hamiltonian problems. These results show that independently chosen local matrices and independently tunable coupling strengths are not necessary for a broad range of Hamiltonian-complexity phenomena.
Comments83 pages, 1 table
