随机张量网络的反集中和状态设计
Guglielmo Lami1, Jacopo De Nardis1, Xhek Turkeshi2
1Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France.
Physical review letters
|February 6, 2025
概括
量子随机张量网络表现出哈尔随机行为,当键尺寸与系统大小多项式扩展时. 这适用于一维和二维系统,显示对单元设计的趋同.
科学领域:
- 量子信息理论 量子信息理论
- 凝聚物质物理学 凝聚物质物理学
- 多体物理多体物理
背景情况:
- 张量网络状态对于模拟量子多体系统至关重要.
- 了解随机张量网络的特性是它们在量子信息中的应用的关键.
- 随机矩阵产物状态 (RMPS) 和预测纠对状态 (PEPS) 是张量网络的重要类别.
研究的目的:
- 为了研究量子随机张量网络状态的脱局属性.
- 在随机矩阵产品状态 (RMPS) 中导出逆参与率 (IPR) 的分析表达式.
- 确定随机张量网络对哈尔随机行为和单元设计的收.
主要方法:
- 导出RMPS的逆参与比率 (IPR) 的确切分析表达式.
- 对不同债券尺寸的重叠概率分布的分析.
- 数值计算的潜力,以测量距离哈尔集团的距离.
- 将分析扩展到二维系统,使用随机预测纠对状态 (PEPS).
主要成果:
- 对于开放和封闭边界条件来说,RMPS的IPR的确切分析表达式得到了推导.
- 对于债券尺寸 χ∼γN,随着 γ 的增加,重叠概率分布与波特-托马斯分布趋同.
- 数字证据显示随机的MPS和PEPS近似哈尔状行为和单位设计的 χ≫sqrt[N].
- 这些属性不管空间维度如何,都保持不变.
结论:
- 具有多项式缩放键维度的随机张量网络完全是Haar反集中的.
- 这些状态接近单元设计,这对于量子信息处理来说是一个重要的发现.
- 该研究提供了对随机张量网络的统计性质的全面理解.
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