发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用ZX演算构建分形多体状态，结合多种方法为三角形族得到无挫折哈密顿量，构造局部变形产生混沌能级统计并嵌入量子多体伤疤，证明ZX演算可用于哈密顿量逆设计，构建相关量子多体伤疤等。
AI 中文摘要
诸如ZX演算这样的图形语言能简洁直观地描述量子过程，已成为电路简化、验证和编译的既定工具。但其作为构建多体状态及其哈密顿量框架的潜力尚待探索。本文引入基于谢尔宾斯基三角形和谢尔宾斯基地毯的ZX图得到的分形多体状态族。这些状态纠缠特性特殊，局部可观测量有分形结构。对于三角形族，结合多种方法得到无挫折哈密顿量，还构造局部变形产生混沌能级统计，将分形ZX状态作为精确量子多体伤疤嵌入能谱主体。结果表明ZX演算可作为哈密顿量逆设计框架，通过图形恒等式构建相关量子多体伤疤等。
英文摘要
Diagrammatic languages such as ZX-calculus provide compact and intuitive descriptions of quantum processes and have become established tools for circuit simplification, verification, and compilation. However, their potential as a framework for constructing many-body states and the Hamiltonians that host them remains largely unexplored. Here, we introduce families of fractal many-body states obtained from ZX-diagrams based on the Sierpiński triangle and Sierpiński carpet. By construction, the underlying graph connectivity imposes atypical subvolume-law minimum-cut upper bounds on entanglement: at most logarithmic scaling for the triangle family and sublinear power-law for the carpet family. By adjusting the free parameters of the ZX-diagram construction, we can tune the actual entanglement scaling: we demonstrate both area-law and logarithmic scaling for the triangle, and both log law and power-law for the carpet. Additionally, their local observables retain fractal-like spatial structure, identifying these states as natural candidates for atypical eigenstates in otherwise thermalizing systems. For the triangle family, we combine parent-Hamiltonian methods, insights from ZX-calculus, and local ZX identities that certify exact annihilation of the target state, producing frustration-free Hamiltonians whose terms admit simple representations in the same diagrammatic language as the states themselves. We then construct a local deformation that produces chaotic level statistics while embedding the fractal ZX state in the bulk of the energy spectrum as an exact quantum many-body scar. Our results demonstrate, through this explicit construction, that ZX-calculus can serve as a framework for Hamiltonian inverse design, in which quantum many-body scars, their local annihilators, and the chaotic Hamiltonians embedding them can be constructed and related through a set of graphical identities.
Comments17 pages, 11 figures
