发表机构
The University of Tokyo; Institute for Physics of Intelligence, The University of Tokyo（东京大学; 东京大学物理智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多体费米子非高斯性度量计算成本高的问题，提出基于矩阵乘积态的完美采样方法，高效计算二阶魔法Rényi熵，并在XXZ链上验证其捕捉高阶关联的能力。
AI 中文摘要
费米子非高斯性是通用量子计算的关键资源，其在量子多体系统中的行为已引起越来越多的关注。最近，一种基于卷积的度量（我们称之为魔法Rényi熵（MRE））被提出作为非高斯性的资源度量，但其评估仅限于小系统，因为计算成本随系统大小呈指数增长。在本工作中，我们开发了一种完美采样方法，用于从矩阵乘积态（MPSs）计算二阶MRE。我们的方法使用有界估计器来控制采样波动，并通过递归扫描直接从输入MPS中抽取样本，这使得我们能够以$\mathcal O(nD^3)$的时间生成每个样本，其中$n$和$D$分别表示模式数和MPS键维。我们在最多128个格点的XXZ链上对我们的方法进行了基准测试，证明MRE能够捕捉大规模下协方差基度量无法访问的复杂高阶关联。这些结果提供了一种计算工具，通过考虑高阶关联来定量评估多体费米子非高斯性。
英文摘要
Fermionic non-Gaussianity is a key resource for universal quantum computation, and its behavior in quantum many-body systems has attracted growing interest. Recently, a convolution-based measure, which we call the magic Rényi entropy (MRE), has been proposed as a resource measure of non-Gaussianity, but its evaluation is limited to small systems due to the computational cost growing exponentially with system size. In this work, we develop a perfect-sampling method to calculate the second-order MRE from matrix product states (MPSs). Our method uses a bounded estimator to control sampling fluctuations and a recursive sweep to draw the samples directly from the input MPS, which allows us to generate each sample with $\mathcal O(nD^3)$ time, where $n$ and $D$ denote the number of modes and MPS bond dimension, respectively. We benchmark our method on the XXZ chain with up to $128$ sites, demonstrating that the MRE captures intricate higher-order correlations at large scales, which are inaccessible to covariance-based measures. These results provide a computational tool that quantitatively evaluates many-body fermionic non-Gaussianity by accounting for higher-order correlations.
Comments21 pages, 11 figures
